lp theory for the multidimensional aggregation equation we consider well posedness of the aggregation equation tu div uv 0 v k u with initial data in input amssym cal p 2 rm bbb r d rm cap l p bbb r d in dimensions 2 and higher we consider radially symmetric kernels where the singularity at the origin is of order x 2 d and prove local well posedness in input amssym cal p 2 bbb r d rm cap l p bbb r d for sufficiently large p ps in the special case of k x x the exponent ps d d 1 is sharp for local well posedness in that solutions can instantaneously concentrate mass for initial data in input amssym cal p 2 bbb r d rm cap l p bbb r d with p ps we also give an osgood condition on the potential k x that guarantees global existence and uniqueness in input amssym cal p 2 bbb r d rm cap l p bbb r d 2010 wiley periodicals inc

obstacle and predator avoidance in a model for flocking abstract the modeling and investigation of the dynamics and configurations of animal groups is a subject of growing attention in this paper we present a deterministic continuum model of flocking and use it to investigate the linearized response of an infinite extent flock to an obstacle or an attacking predator we show that the steady state flock response is in the form of density disturbances that resemble mach cones whose configuration is determined by the anisotropic propagation of waves through the flock we analytically and numerically test relations that predict the mach wedge angles disturbance heights and wake widths we find that these expressions are insensitive to many of the parameters of the model

time adaptive variational integrators a space time geodesic approach abstract the goal of this paper is to show that the space time geodesic approach of classical mechanics can be used to generate a time adaptive variational integration scheme the only assumption we make is that the lagrangian for the system is in a separable form the geometric structure which is preserved in the integration scheme is made explicit and the algorithm is illustrated with simulation for a compact case a non compact case a chaotic system which arises as a perturbation of an integrable system and the figure eight solution for a three body problem

on the problem of reconstructing an unknown topology via locality properties of the wiener filter determining interrelatedness structure of various entities from multiple time series data is of significant interest to many areas knowledge of such a structure can aid in identifying cause and effect relationships clustering of similar entities identification of representative elements and model reduction the majority of existing results are based on correlation based indices which effectively assume a static relationship between the time series data and are not suitable for detecting interrelatedness when the time series are dynamically related or when the time series involve loops in this paper a methodology for identifying the interrelatedness structure of dynamically related time series data is presented that also allows for the presence of loops in the connectivity structure a linear dynamic graph model is presented where it is assumed that each time series data is the sum of an independent stochastic noise source and a dynamically weighted sum of other time series data a link is assumed to be present between two time series if the weight of a time series which is a linear time invariant filter is nonzero in the formation of the other reconstruction of the link connectivity structure under various scenarios is considered it is shown that when the linear dynamic graph is allowed to admit non causal weights then the links structure can be recovered with the possibility of identifying spurious connections however it is shown that the spurious links remain local where a spurious link is restricted to be within one hop of a true link furthermore strategies for exact reconstruction of the link structure when the weights are restricted to be causal are developed the main tools for determining the network topology are based on variations of wiener filtering a significant insight provided by the article is that in the class of network models considered in the paper the wiener filter estimating a stochastic process based on other processes remains local in the sense that the wiener filter utilizes only measurements local to the node being estimated

a new interaction potential for swarming models abstract we consider a self propelled particle system which has been used to describe certain types of collective motion of animals such as fish schools and bird flocks interactions between particles are specified by means of a pairwise potential repulsive at short ranges and attractive at longer ranges the exponentially decaying morse potential is a typical choice and is known to reproduce certain types of collective motion observed in nature particularly aligned flocks and rotating mills we introduce a class of interaction potentials that we call quasi morse for which flock and rotating mills states are also observed numerically however in that case the corresponding macroscopic equations allow for explicit solutions in terms of special functions with coefficients that can be obtained numerically without solving the particle evolution we compare the obtained solutions with long time dynamics of the particle systems and find a close agreement for several types of flock and mill solutions

finite size scaling analysis and dynamic study of the critical behavior of a model for the collective displacement of self driven individuals the vicsek model vm t vicsek et al phys rev lett 75 1226 1995 for the description of the collective behavior of self driven individuals assumes that each of them adopts the average direction of movement of its neighbors perturbed by an external noise a second order transition between a state of ordered collective displacement low noise limit and a disordered regime high noise limit was found early on however this scenario has recently been challenged by gr egory and chat e g gr egory and h chat e phys rev lett 92 025702 2004 who claim that the transition of the vm may be of first order by performing extensive simulations of the vm which are analyzed by means of both finite size scaling methods and a dynamic scaling approach we unambiguously demonstrate the critical nature of the transition furthermore the complete set of critical exponents of the vm in d 2 dimensions is determined by means of independent methods i e stationary and dynamic measurements we provide two tests showing that the standard hyperscaling relationship d ensuremath nu ensuremath 2 ensuremath beta ensuremath gamma holds where ensuremath beta ensuremath nu and ensuremath gamma are the order parameter correlation length and susceptibility critical exponents respectively furthermore we established that at criticality the correlation length grows according to ensuremath xi ensuremath sim t 1 z with z ensuremath simeq 1 27 3 independently of the degree of order of the initial configuration in marked contrast with the behavior of the xy model

optimal multi agent coordination under tree formation constraints this paper presents a framework for studying the centralized optimal multi agent coordination problem under tree formation constraints the geodesic equations characterizing the optimal coordinated motions are derived in a suitably chosen coordinate system for general tree formation constraints the solutions to these equations however may fail to be optimal once extended beyond certain points called the conjugate points due to the failure of the second order optimality condition for the particular class of star formations two methods for computing the conjugate points along a natural candidate solution are introduced using these methods we derive analytically the conjugate points as well as the better solutions once the candidate solution is extended beyond its first conjugate point the optimal centralized coordinated motions derived in this paper will yield a performance lower bound for those generated by decentralized algorithms

asymptotically optimal decentralized control for large population stochastic multiagent systems the interaction of interest coupled decision makers and the uncertainty of individual behavior are prominent characteristics of multiagent systems mas how to break through the framework of conventional control theory which aims at single decision maker and single decision objective and to extend the methodology and tools in the stochastic adaptive control theory to analyze mas are of great significance in this paper a preliminary exploration is made in this direction and the decentralized control problem is considered for large population stochastic mas with coupled cost functions different from the deterministic discounted costs in the existing differential game models a time averaged stochastic cost function is adopted for each agent the decentralized control law is constructed based on the state aggregation method and tracking like quadratic optimal control by using probability limit theory the stability and optimality of the closed loop system are analyzed the main contributions of this paper include the following points 1 the concepts of asymptotic nash equilibrium in probability and almost surely respectively are introduced and the relationship between these concepts is illuminated which provide necessary tools for analyzing the optimality of the decentralized control laws 2 the closed loop system is shown to be almost surely uniformly stable and bounded independently of the number of agents n 3 the population state average psa is shown to converge to the infinite population mean ipm trajectory in the sense of both l2 norm and time average almost surely as n increases to infinity 4 the decentralized control law is designed and shown to be almost surely asymptotically optimal the cost of each agent based on local measurements converges to that based on global measurements almost surely as n increases to infinity

distributed nonlinear control of mobile autonomous multi agents abstract this paper studies the distributed nonlinear control of mobile autonomous agents with variable and directed topology a new distributed nonlinear design scheme is presented for multi agent systems modeled by double integrators with the new design the outputs of the controlled agents asymptotically converge to each other as long as a mild connectivity condition is satisfied moreover the velocity derivative of the output of each agent can be restricted to be within any specified neighborhood of the origin which is of practical interest for systems under such physical constraint the new design is still valid if one of the agents is a leader and the control objective is to achieve leader following as an illustration of the generality and effectiveness of the presented methodology the formation control of a group of unicycle mobile robots with nonholonomic constraints is revisited instead of assuming the point robot model the unicycle model is transformed into two double integrators by dynamic feedback linearization and the proposed distributed nonlinear design method is used to overcome the singularity problem caused by the nonholonomic constraint by properly restricting the velocities simulation results are included to illustrate the theoretical results

promoting collective motion of self propelled agents by discarding short range interactions abstract we study the collective motion of self propelled agents with the restricted view the field of view of each agent is an annulus bounded by the outer radius r and inner radius r where is a tunable parameter we find that there exists an optimal value of leading to the highest degree of direction consensus this phenomenon indicates that there exists superfluous communication in the collective motion of self propelled agents and short range interactions hinder the direction consensus of the system the value of optimal decreases as the absolute velocity increases while it increases as the outer radius r and the system size increase for a fixed value of direction consensus is enhanced when the absolute velocity is small the outer radius or the system size is large

streaming disruptive interference and power law behavior in the exit dynamics of confined pedestrians we analyze the exit dynamics of pedestrians who are initially confined in a room pedestrians are modeled as cellular automata and compete to escape via a known exit at the soonest possible time a pedestrian could move forward backward left or right within each iteration time depending on adjacent cell vacancy and in accordance with simple rules that determine the compulsion to move and physical capability relative to his neighbors the arching signatures of jamming were observed and the pedestrians exited in bursts of various sizes power law behavior is found in the burst size frequency distribution for exit widths w greater than one cell dimension w 1 the slope of the power law curve varies with w from 1 3092 w 2 to 1 0720 w 20 streaming which is a diffusive behavior arises in large burst sizes and is more likely in a single exit room with w 1 and leads to a counterintuitive result wherein an average exit throughput q is obtained that is higher than with w 2 3 or 4 for a two exit room w 1 q is not greater than twice the yield of a single exit room if the doors are not separated far enough 4w q becomes even significantly less due to a collective slow down that emerges among pedestrians crossing in each other s path disruptive interference effect for the same w and door number q is also higher with relaxed pedestrians than with anxious ones

damage spreading and critical exponents for model a ising dynamics using damage spreading and heat bath dynamics we study the ising model in 2 and 3 dimensions with non conservative dynamics our algorithm differs in some important points from previous ones which makes it rather efficient we give estimates for the exponent z which seem to be the most precise published so far 2 172 0 006 for d 2 2 032 0 004 for d 3 we also give precise estimates of the exponent introduced by janssen et al z phys b 73 1989 539 and of analogous but in principle independent exponents we find surprisingly that some of the latter agree with and give an explanation for this

the structure of sally modules towards a theory of non cohen macaulay cases abstract sally modules of m primary ideals in a generalized cohen macaulay and or buchsbaum local ring a m are investigated the structure theorems of sally modules of rank one given by goto et al 2008 gno1 gno2 in the case where a is a cohen macaulay local ring are generalized

mean field theory for a simple model of evolution a simple dynamical model for darwinian evolution on its slowest time scale is analyzed its mean field theory is formulated and solved a random neighbor version of the model is simulated as is a one dimensional version in one dimension the dynamics can be described in terms of a repetitious random walker and anomalous diffusion with exponent 0 4 in all cases the model self organizes to a robust critical attractor

adaptive geometric integrators for hamiltonian problems with approximate scale invariance we consider adaptive geometric integrators for the numerical integration of hamiltonian systems with greatly varying time scales a time regularization is considered using either the sundman or the poincare transformation in the latter case this gives a new hamiltonian which is usually separable but with one of the parts not always exactly solvable this system can be numerically integrated with a splitting scheme where each part can be computed using a symplectic implicit or explicit method preserving the qualitative properties of the exact solution in this case a backward error analysis for the numerical integration is presented for a one dimensional near singular problem this analysis reveals a strong dependence of the performance of the method with the choice of the monitor function g which is also observed when using other symmetric nonsymplectic integrators we also show how this dependence greatly increases with the order of the numerical integrator used the optimal choice corresponds to the function g which nearly preserves the scaling invariance of the system numerical examples supporting this result are presented in some cases a canonical transformation can also be considered making the system more regular or easy to compute and this is also illustrated with some examples

gas kinetic derivation of navier stokes like traffic equations macroscopic traffic models have recently been severely criticized to base on lax analogies only and to have a number of deficiencies therefore this paper shows how to construct a logically consistent fluid dynamic traffic model from basic laws for the acceleration and interaction of vehicles these considerations lead to the gas kinetic traffic equation of paveri fontana its stationary and spatially homogeneous solution implies equilibrium relations for the fundamental diagram the variance density relation and other quantities which are partly difficult to determine empirically paveri fontana s traffic equation allows the derivation of macroscopic moment equations which build a system of non closed equations this system can be closed by the well proved method of chapman and enskog which leads to euler like traffic equations in zeroth order approximation and to navier stokes like traffic equations in first order approximation the latter are finally corrected for the finite space requirements of vehicles it is shown that the resulting model is able to withstand the above mentioned criticism

three dimensional circular formations via set stabilization the paper addresses distributed stabilization of a class of circular formations for steered kinematic particles in three dimensional euclidean space information exchange between the particles is modeled by a bidirectional graph which is assumed to have a spanning tree distributed control design is based on a hierarchical approach that relies on set stabilization and a reduction principle for asymptotic stability of closed sets the approach allows to solve for different formation specifications in a decoupled manner

integral closedness of complete intersection ideals the aim of this paper is to give some structure theorem of certain integrally closed ideals in noetherian rings let a be a noetherian ring and i an ideal of a then an element x of a is said to be integral over z if x satisfies an equation x c x c 0 in a with ci e i the integral closure i of z is by definition the set of elements in a which are integral over z and the ideal z is called integrally closed if f i let ua z resp ht i denote the smallest number of elements in systems of generators for z resp the height of i let min a z be the set of minimal prime divisors of i in this paper we shall study the problem when the ideals z of a such that ua z ht z are integrally closed and our result is stated as follows

links of prime ideals and their rees algebras abstract in a previous paper we exhibited the somewhat surprising property that most direct links of prime ideals in gorenstein rings are equimultiple ideals with reduction number 1 this led to the construction of large families of cohen macaulay rees algebras the first goal of this paper is to extend this result to arbitrary cohen macaulay rings the means of the proof are changed since one cannot depend so heavily on linkage theory we then study the structure of the rees algebra of these links more specifically we describe their canonical module in sufficient detail to be able to characterize self linked prime ideals in the last section multiplicity estimates for classes of such ideals are established

symplectic energy momentum preserving variational integrators the purpose of this paper is to develop variational integrators for conservative mechanical systems that are symplectic and energy and momentum conserving to do this a space time view of variational integrators is employed and time step adaptation is used to impose the constraint of conservation of energy criteria for the solvability of the time steps and some numerical examples are given

self organization in systems of self propelled particles we investigate a discrete model consisting of self propelled particles that obey simple interaction rules we show that this model can self organize and exhibit coherent localized solutions in one and in two dimensions in one dimension the self organized solution is a localized flock of finite extent in which the density abruptly drops to zero at the edges in two dimensions we focus on the vortex solution in which the particles rotate around a common center and show that this solution can be obtained from random initial conditions even in the absence of a confining boundary furthermore we develop a continuum version of our discrete model and demonstrate that the agreement between the discrete and the continuum model is excellent

spontaneously ordered motion of self propelled particles we study a biologically inspired inherently non equilibrium model consisting of self propelled particles in the model particles move on a plane with a velocity of constant magnitude they locally interact with their neighbours by choosing at each timestep a velocity direction equal to the average direction of their neighbours thus in the limit of vanishing velocities the model becomes analogous to a monte carlo realization of the classical xy ferromagnet we show by large scale numerical simulations that unlike in the equilibrium xy model a long range ordered phase characterized by non vanishing net flow emerges in this system in a phase space domain bordered by a critical line along which the fluctuations of the order parameter diverge the corresponding phase diagram as a function of two parameters the amplitude of noise and the average density of the particles is calculated and is found to have the form we also find that scales as a function of the external bias h field or wind according to a power law in the ordered phase the system shows long range correlated fluctuations and 1 f noise

stability properties of the collective stationary motion of self propelling particles with conservative kinematic constraints in our previous papers we proposed a continuum model for the dynamics of the systems of self propelling particles with conservative kinematic constraints on the velocities we have determined a class of stationary solutions of this hydrodynamic model and have shown that two types of stationary flow linear and axially symmetric vortical flow are possible in this paper we consider the stability properties of these stationary flows we show using a linear stability analysis that the linear solutions are neutrally stable with respect to the imposed velocity and density perturbations a similar analysis of the stability of the vortical solution is found to be not conclusive

multiparticle random walks on a deformable medium multiparticle random walks on a deformable medium have been investigated in 2 1 dimensions the time evolution of the particle distribution is studied the results show that the randomly distributed particles in the beginning will be self organized into a cluster pattern in the intermediate stage and then return to the random distribution pattern in the late stage the dependence of the clustering degree on the stiffness parameter of medium ensuremath alpha stability parameter of systems ensuremath beta and average particle density ensuremath rho 0 is also investigated there exists an optimal clustering stability ensuremath beta p at which the system has the strongest clustering ability and corresponds to a maximum clustering coefficient ensuremath gamma p the dependence of the optimal clustering coefficient ensuremath gamma p on the stiffness ensuremath alpha and particle density ensuremath rho 0 is obtained and the landscape of the medium generated by particles is also investigated

statistical properties of aggregation with injection we study a generalized aggregation process in which charged particles diffuse and coalesce randomly on a lattice for one dimensional and mean field models we show that there exists a statistically invariant steady state when randomly charged particles are continuously injected the steady state charge distribution obeys a power law with the exponent depending both on the type of the injection and on the spatial dimension the response of the system to a perturbation i e relaxation is characterized by either a power law decay t 1 or a compressed exponential decay exp t 1

impulsive multiconsensus of second order multiagent networks using sampled position data a multiconsensus problem of multiagent networks is solved in this paper where multiconsensus refers to that the states of multiple agents in each subnetwork asymptotically converge to an individual consistent value when there exist information exchanges among subnetworks a distributed impulsive protocol is proposed to achieve multiconsensus of second order multiagent networks in terms of three categories 1 stationary multiconsensus 2 the first dynamic multiconsensus and 3 the second dynamic multiconsensus this impulsive protocol utilizes only sampled position data and is implemented at sampling instants for those three categories of multiconsensus the control parameters in the impulsive protocol are designed respectively moreover necessary and sufficient conditions are derived under which each multiconsensus can be reached asymptotically several simulations are finally provided to demonstrate the effectiveness of the obtained theoretical results

phase transitions in self driven many particle systems and related non equilibrium models a network approach we investigate the conditions that produce a phase transition from an ordered to a disordered state in a family of models of two dimensional elements with a ferromagnetic like interaction this family is defined to contain under the same framework among others the xy model and the self driven particles model introduced by vicsek et al each model is distinguished only by the rules that determine the set of elements with which each element interacts we propose a new member of the family the vectorial network model in which a given fraction of the elements interact through direct random connections this model is analogous to an xy system on a network and as such can be of interest for a wide range of problems it captures the main aspects of the interaction dynamics that produce the phase transition in other models of the family the network approach allows us to show analytically the existence of a phase transition in this vectorial network model and to compute its relevant parameters for the case in which all elements are randomly connected finally we study numerically the conditions required for a phase transition to exist for different members of the family our results show that a qualitatively equivalent phase transition appears whenever even a small amount of long range interactions are present or built over time regardless of other equilibrium or non equilibrium properties of the system

clustering in a network of non identical and mutually interacting agents clustering is a phenomenon that may emerge in multi agent systems through self organization groups arise consisting of agents with similar dynamic behaviour it is observed in fields ranging from

constrained consensus of asynchronous discrete time multi agent systems with time varying topology the union graph is assumed to be strongly connected over each finite interval an approach is proposed to transform the original network to a synchronous one we show that the linear part converges and the projection error vanishes over time in this paper the constrained consensus problem is studied for asynchronous discrete time multi agent system where each agent needs to lie in a closed convex constraint set while reaching consensus the communication graphs are assumed to be directed unbalanced dynamically changing in addition their union graph is assumed to be strongly connected among certain intervals of finite length to deal with the asynchronous communications among agents the original asynchronous system is equivalently transformed to the synchronous one by adding new agents by employing the properties of the projection on the convex sets the distance from the states of the agents in the newly constructed system to the intersection set of all agents constraint sets is estimated based on this estimation the original system is proven to reach consensus by showing that the linear parts of the newly constructed systems converge and the nonlinear parts vanish over time finally two numerical examples are provided to show the effectiveness of the theoretical results

distributed circular formation stabilization for dynamic unicycles this paper investigates the problem of designing distributed control laws making a group of dynamic unicycles converge to a common circle of prespecified radius whose center is stationary but dependent on the initial conditions and travel around the circle in a desired direction the vehicles are required to converge to a formation on the circle expressed by desired separations and ordering of the unicycles the information exchange between unicycles is modelled by a directed graph which is assumed to have a spanning tree a hierarchical approach is proposed which simplifies the control design by decoupling the problem of making the unicycles converge to a common circle from the problem of stabilizing the formation

flocks herds and schools a quantitative theory of flocking we present a quantitative continuum theory of flocking the collective coherent motion of large numbers of self propelled organisms in agreement with everyday experience our model predicts the existence of an ordered phase of flocks in which all members of even an arbitrarily large flock move together with the same mean velocity stackrel ensuremath rightarrow v ensuremath ne 0 this coherent motion of the flock is an example of spontaneously broken symmetry no preferred direction for the motion is picked out a priori in the model rather each flock is allowed to and does spontaneously pick out some completely arbitrary direction to move in by analyzing our model we can make detailed quantitative predictions for the long distance long time behavior of this broken symmetry state the goldstone modes associated with this spontaneously broken rotational symmetry are fluctuations in the direction of motion of a large part of the flock away from the mean direction of motion of the flock as a whole these goldstone modes mix with modes associated with conservation of bird number to produce propagating sound modes these sound modes lead to enormous fluctuations of the density of the flock far larger at long wavelengths than those in e g an equilibrium gas our model is similar in many ways to the navier stokes equations for a simple compressible fluid in other ways it resembles a relaxational time dependent ginsburg landau theory for an n d component isotropic ferromagnet in spatial dimensions dg4 the long distance behavior is correctly described by a linearized theory and is equivalent to that of an unusual but nonetheless equilibrium model for spin systems for dl4 nonlinear fluctuation effects radically alter the long distance behavior making it different from that of any known equilibrium model in particular we find that in d 2 where we can calculate the scaling exponents exactly flocks exhibit a true long range ordered spontaneously broken symmetry state in contrast to equilibrium systems which cannot spontaneously break a continuous symmetry in d 2 the mermin wagner theorem we make detailed predictions for various correlation functions that could be measured either in simulations or by quantitative imaging of real flocks we also consider an anisotropic model in which the birds move preferentially in an easy e g horizontal plane and make analogous but quantitatively different predictions for that model as well for this anisotropic model we obtain exact scaling exponents for all spatial dimensions including the physically relevant case d 3

brief paper second order consensus in multi agent dynamical systems with sampled position data this paper studies second order consensus in multi agent dynamical systems with sampled position data a distributed linear consensus protocol with second order dynamics is designed where both the current and some sampled past position data are utilized it is found that second order consensus in such a multi agent system cannot be reached without any sampled position data under the given protocol while it can be achieved by appropriately choosing the sampling period a necessary and sufficient condition for reaching consensus of the system in this setting is established based on which consensus regions are then characterized it is shown that if all the eigenvalues of the laplacian matrix are real then second order consensus in the multi agent system can be reached for any sampling period except at some critical points depending on the spectrum of the laplacian matrix however if there exists at least one eigenvalue of the laplacian matrix with a nonzero imaginary part second order consensus cannot be reached for sufficiently small or sufficiently large sampling periods in such cases one nevertheless may be able to find some disconnected stable consensus regions determined by choosing appropriate sampling periods finally simulation examples are given to verify and illustrate the theoretical analysis

stochastic flocking dynamics of the cucker smale model with multiplicative white noises we present a strong asymptotic stochastic flocking estimate for the stochastically perturbed cucker smale model we characterize a form of multiplicative white noises and present sufficient conditions on the control parameters to guarantee the almost sure exponential convergence toward constant equilibrium states when the strength of multiplicative noises is sufficiently large we show that the strong stochastic flocking occurs even for negative communication weights

nonsmooth coordination and geometric optimization via distributed dynamical systems emerging applications for networked and cooperative robots motivate the study of motion coordination for groups of agents for example it is envisioned that groups of agents will perform a variety of useful tasks including surveillance exploration and environmental monitoring this paper deals with basic interactions among mobile agents such as move away from the closest other agent or move toward the furthest vertex of your own voronoi polygon these simple interactions amount to distributed dynamical systems because their implementation requires only minimal information about neighboring agents we characterize the close relationship between these distributed dynamical systems and the disk covering and sphere packing cost functions from geometric optimization our main results are as follows i we characterize the smoothness properties of these geometric cost functions ii we show that the interaction laws are variations of the nonsmooth gradient of the cost functions and iii we establish various asymptotic convergence properties of the laws the technical approach relies on concepts from computational geometry nonsmooth analysis and nonsmooth stability theory

finite time convergent gradient flows with applications to network consensus this paper introduces the normalized and signed gradient dynamical systems associated with a differentiable function extending recent results on nonsmooth stability analysis we characterize their asymptotic convergence properties and identify conditions that guarantee finite time convergence we discuss the application of the results to consensus problems in multi agent systems and show how the proposed nonsmooth gradient flows achieve consensus in finite time

hierarchical cluster structures in a one dimensional swarm oscillator model swarm oscillator model derived by one of the authors tanaka where interacting motile elements form various kinds of patterns is investigated we particularly focus on the cluster patterns in one dimensional space we mathematically derive all static and stable configurations in final states for a particular but a large set of parameters in the derivation we introduce renormalized expression of this model we find that the static final states are hierarchical cluster structures in which a cluster consists of smaller clusters in a nesting manner

deterministic models for traffic jams abstract we study several deterministic one dimensional traffic models for integer positions and velocities we find the typical high and low density phases separated by a simple transition if positions and velocities are continuous variables the model shows self organized critically driven by the slowest car

control of frictional dynamics of a one dimensional particle array control of frictional forces is required in many applications of tribology while the problem is approached by chemical means traditionally a recent approach was proposed to control the system mechanically to tune frictional responses we design feedback control laws for a one dimensional particle array sliding on a surface subject to friction the frenkel kontorova model describing the dynamics is a nonlinear interconnected system and the accessible control elements are average quantities only we prove local stability of equilibrium points of the un controlled system in the presence of linear and nonlinear particle interactions respectively we then formulate a tracking control problem whose control objective is for the average system to reach a designated targeted velocity using accessible elements sufficient stabilization conditions are explicitly derived for the closed loop error systems using the lyapunov theory based methods simulation results show satisfactory performances the results can be applied to other physical systems whose dynamics is described by the frenkel kontorova model

distributed network optimization with heuristic rational agents a network of distributed agents wants to minimize a global cost given by a sum of local terms involving nonlinear convex functions of self and neighboring variables agents update their variables at random times by observing the values of neighboring agents and applying a random heuristic rule intent on minimizing the local cost with respect to their own variables the heuristic rules are rational in that their average result is the actual optimal action with respect to the given values of neighboring variables by identifying heuristic rational optimization with stochastic coordinate descent it is shown that all agents visit a neighborhood of the optimal cost infinitely often with probability 1 an exponential probability bound on the worst deviation from optimality between visits to near optimal operating points is also derived commonly used models of consensus and opinion propagation in social networks markov random field estimation in wireless sensor networks and cohesive foraging of animal herds are cast in the language of heuristic rational optimization numerical simulations for these three examples are presented to corroborate analytical results

error analysis of variational integrators of unconstrained lagrangian systems an error analysis of variational integrators is obtained by blowing up the discrete variational principles all of which have a singularity at zero time step divisions by the time step lead to an order that is one less than observed in simulations a deficit that is repaired with the help of a new past future symmetry

global synchronization for a class of dynamical complex networks abstract this paper is concerned with the problem of global synchronization for a class of dynamical complex networks composed of general lur e systems based on the absolute stability theory and the kalman yakubovich popov kyp lemma sufficient conditions are established to guarantee global synchronization of dynamical networks with complex topology directed and weighted couplings several global synchronization criteria formulated in the form of linear matrix inequalities lmis or frequency domain inequalities are also proposed for undirected dynamical networks in order to obtain global results no linearization technique is involved through derivation of the synchronization criteria numerical examples are provided to demonstrate the effectiveness of the proposed results

avoiding collisions in flocks among the many models for flocking systems of interacting particles the one introduced by cucker and smale has attracted attention due to the fact that a convergence to flocking i e to a common velocity could be established depending on conditions on the initial state of the system in this note we extend this model by adding to it a repelling force between particles we show that for this modified model convergence to flocking is established along the same lines while in addition avoidance of collisions i e the respect of a minimal distance between particles is ensured

a class of attractions repulsion functions for stable swarm aggregations in this brief article we consider an m member individual based continuous time swarm model in an n dimensional space and extend the results in gazi and passino 2003 by specifying a general class of attraction repulsion functions that can be used to achieve swarm aggregation these functions are odd functions that have terms for attraction and repulsion acting in opposite directions in compliance with real biological swarms we present stability analysis for several cases of the functions considered to characterize swarm cohesiveness size and ultimate motions while in a cohesive group moreover we show how the model can be extended for achieving formation control furthermore we discuss how the attraction repulsion functions can be modified to incorporate the finite body size of the swarm members numerical simulations are also presented for illustration purposes

observer design for tracking consensus in second order multi agent systems fractional order less than two this technical note studies the leader following tracking consensus problem of a class of multi agent systems where the dynamics of the leader is described by second order systems in order to track the states of the leader observers for the followers are designed by fractional order multi agent systems where the relative velocity information is unavailable it is interestingly found that the followers can track the leader with second order dynamics even if the fractional order is less than two by only using the position information of the local neighbors which is different from the existing results a novel fractional order observer is first proposed whose order is surprisingly less than the original leader system it is also shown that leader following consensus can be ensured if some carefully selected followers are informed and the relative position based protocols are appropriately designed with fractional order being between one and two a necessary and sufficient condition for the leader following consensus in multi agent systems without control input delay is proposed the results are then extended to the case with constant control input delay it is found that in both cases the real and imaginary parts of the eigenvalues of the augmented laplacian matrix of the topology play an important role in achieving consensus

brief paper decentralized coordination of autonomous swarms using parallel gibbs sampling in this paper we present analysis of a discrete time decentralized stochastic coordination algorithm for a group of mobile nodes called an autonomous swarm on a finite spatial lattice all nodes take their moves by sampling in parallel their locally perceived gibbs distributions corresponding to a pairwise nearest neighbor potential the algorithm has no explicit requirements on the connectedness of the underlying information graph which varies with the swarm configuration it is established that with an appropriate annealing schedule the algorithm results in swarm configurations converging to the global minimizers of a modified potential energy function the extent of discrepancy between the modified and original potential energy functions is determined by the maximum node travel between time steps and when such distance is small the ultimate swarm configurations are close to the global minimizers of the original potential energy simulation results are further presented to illustrate the capability of the sampling algorithm in approximate global optimization for swarms

multisymplectic geometry variational integrators and nonlinear pdes this paper presents a geometric variational approach to continuous and discrete mechanics and field theories using multisymplectic geometry we show that the existence of the fundamental geometric structures as well as their preservation along solutions can be obtained directly from the variational principle in particular we prove that a unique multisymplectic structure is obtained by taking the derivative of an action function and use this structure to prove covariant generalizations of conservation of symplecticity and noether s theorem natural discretization schemes for pdes which have these important preservation properties then follow by choosing a discrete action functional in the case of mechanics we recover the variational symplectic integrators of veselov type while for pdes we obtain covariant spacetime integrators which conserve the corresponding discrete multisymplectic form as well as the discrete momentum mappings corresponding to symmetries we show that the usual notion of symplecticity along an infinite dimensional space of fields can be naturally obtained by making a spacetime split all of the aspects of our method are demonstrated with a nonlinear sine gordon equation including computational results and a comparison with other discretization schemes

distributed leader follower flocking control for multi agent dynamical systems with time varying velocities abstract using tools from algebraic graph theory and nonsmooth analysis in combination with ideas of collective potential functions velocity consensus and navigation feedback a distributed leader follower flocking algorithm for multi agent dynamical systems with time varying velocities is developed where each agent is governed by second order dynamics the distributed leader follower algorithm considers the case in which the group has one virtual leader with time varying velocity for each agent i this algorithm consists of four terms the first term is the self nonlinear dynamics which determines the final time varying velocity the second term is determined by the gradient of the collective potential between agent i and all of its neighbors the third term is the velocity consensus term and the fourth term is the navigation feedback from the leader to avoid an impractical assumption that the informed agents sense all the states of the leader the new designed distributed algorithm is developed by making use of observer based pinning navigation feedback in this case each informed agent only has partial information about the leader yet the velocity of the whole group can still converge to that of the leader and the centroid of those informed agents having the leader s position information follows the trajectory of the leader asymptotically finally simulation results are presented to demonstrate the validity and effectiveness of the theoretical analysis surprisingly it is found that the local minimum of the potential function may not form a commonly believed lattice

an ode model of the motion of pelagic fish a system of ordinary differential equations odes is derived from a discrete system of vicsek czirok et al phys rev lett 75 6 1226 1229 1995 describing the motion of a school of fish classes of linear and stationary solutions of the odes are found and their stability explored using equivariant bifurcation theory the existence of periodic and toroidal solutions is also proven under deterministic perturbations and structurally stable heteroclinic connections are found applications of the model to the migration of the capelin a pelagic fish that undertakes an extensive migration in the north atlantic are discussed and simulation of the odes presented

variational integrators and the newmark algorithm for conservative and dissipative mechanical systems the purpose of this work is twofold first we demonstrate analytically that the classical newmark family as well as related integration algorithms are variational in the sense of the veselov formulation of discrete mechanics such variational algorithms are well known to be symplectic and momentum preserving and to often have excellent global energy behavior this analytical result is veried through numerical examples and is believed to be one of the primary reasons that this class of algorithms performs so well second we develop algorithms for mechanical systems with forcing and in particular for dissipative systems in this case we develop integrators that are based on a discretization of the lagrange d alembert principle as well as on a variational formulation of dissipation it is demonstrated that these types of structured integrators have good numerical behavior in terms of obtaining the correct amounts by which the energy changes over the integration run

explicit time reversible adaptive step size control adaptive step size control is difficult to combine with geometric numerical integration as classical step size control is based on past information only time symmetry is destroyed and with it the qualitative properties of the method in this paper we develop completely explicit reversible symmetry preserving adaptive step size selection algorithms for geometric numerical integrators such as the stormer verlet method a new step density controller is proposed and analyzed using backward error analysis and reversible perturbation theory for integrable reversible systems we show that the resulting adaptive method nearly preserves all action variables and in particular the total energy for hamiltonian systems it has the same excellent long term behavior as that obtained when constant steps are used with variable steps however both accuracy and efficiency are greatly improved

new tools for characterizing swarming systems a comparison of minimal models abstract we compare three simple models that reproduce qualitatively the emergent swarming behavior of bird flocks fish schools and other groups of self propelled agents by using a new set of diagnosis tools related to the agents spatial distribution two of these correspond in fact to different implementations of the same model which had been previously confused in the literature all models appear to undergo a very similar order to disorder phase transition as the noise level is increased if we only compare the standard order parameter which measures the degree of agent alignment when considering our novel quantities however their properties are clearly distinguished unveiling previously unreported qualitative characteristics that help determine which model best captures the main features of realistic swarms additionally we analyze the agent clustering in space finding that the distribution of cluster sizes is typically exponential at high noise and approaches a power law as the noise level is reduced this trend is sometimes reversed at noise levels close to the phase transition suggesting a non trivial critical behavior that could be verified experimentally finally we study a bi stable regime that develops under certain conditions in large systems by computing the probability distributions of our new quantities we distinguish the properties of each of the coexisting metastable states our study suggests new experimental analyses that could be carried out to characterize real biological swarms

invariance principles allowing of non lyapunov functions for estimating attractor of discrete dynamical systems this technical note establishes several versions of invariance principles for describing the eventual dynamical behaviors of discrete dynamical systems instead of the requirement of the so called lyapunov functions in the classical lasalle invariance principle some more relaxed conditions are imported the established invariance principles thus can be applied to a more general class of discrete dynamical systems for classifying their orbits into two categories based on the eventual dynamical behaviors and the proposed classification scheme is suitable for theoretically and numerically estimating the local or global attractors produced by the discrete dynamical systems the practical usefulness of the analytical results is verified by systematically investigating several representative discrete systems

stabilization of a class of dynamical complex networks based on decentralized control abstract this paper deals with a stabilization problem for a class of dynamical complex networks with each node being a general lur e system based on a lur e postnikov function and a special decentralized control strategy the problem of designing a linear feedback controller such that states of all nodes are globally stabilized onto an expected homogeneous state is addressed a controller design method based on parameter dependent lur e postnikov function is proposed in order to reduce the conservativeness and the controller can be constructed via feasible solutions of a certain set of linear matrix inequalities lmis a dynamical network composed of identical chua s circuits is adopted as a numerical example to demonstrate the effectiveness of the proposed results

double hopf bifurcation and quasi periodic attractors in delay coupled limit cycle oscillators abstract we investigate the double hopf bifurcation at zero equilibrium point firstly we give the critical values of hopf and double hopf bifurcations secondly we implement the normal form method and the center manifold theory for delay coupled limit cycle oscillators and derive the universal unfolding and a complete bifurcation diagram of the system thirdly many interesting phenomena such as attractive periodic motion and three dimensional invariant torus are observed using numerical simulation finally the normal forms of several strong resonant cases are listed

stability analysis of swarms in this note we specify an individual based continuous time model for swarm aggregation in n dimensional space and study its stability properties we show that the individuals autonomous agents or biological creatures will form a cohesive swarm in a finite time moreover we obtain an explicit bound on the swarm size which depends only on the parameters of the swarm model

asymptotic behavior of parameter ideals in generalized cohen macaulay modules abstract the purpose of this paper is to give affirmative answers to two open questions as follows let r m be a generalized cohen macaulay noetherian local ring both questions the first question was raised by m rogers m rogers the index of reducibility for parameter ideals in low dimension j algebra 278 2004 571 584 and the second one is due to s goto and h sakurai s goto h sakurai the equality i 2 q i in buchsbaum rings rend sem mat univ padova 110 2003 25 56 ask whether for every parameter ideal q contained in a high enough power of the maximal ideal m the following statements are true 1 the index of reducibility n r q r is independent of the choice of q and 2 i 2 q i where i q r m

the equality i2 qi in sequentially cohen macaulay rings let r be a sequentially cohen macaulay local ring and assume that dimr 2 or that dimr 1 and e r 1 then the equality i2 qi holds true for every good parameter ideal q of r contained in a sufficiently high power of the maximal ideal m where i q rm the structure of the graded rings gr i n 0in in 1 r i n 0in and r i n zin associated to i is explored in connection to their sequential cohen macaulayness

variational time integrators the purpose of this paper is to review and further develop the subject of variational integration algorithms as it applies to mechanical systems of engineering interest in particular the conservation properties of both synchronous and asynchronous variational integrators avis are discussed in detail we present selected numerical examples which demonstrate the excellent accuracy conservation and convergence characteristics of avis in these tests avis are found to result in substantial speed ups at equal accuracy relative to explicit newmark a mathematical proof of convergence of the avis is also presented in this paper finally we develop the subject of horizontal variations and configurational forces in discrete dynamics this theory leads to exact path independent characterizations of the configurational forces acting on discrete systems notable examples are the configurational forces acting on material nodes in a finite element discretisation and the j integral at the tip of a crack in a finite element mesh

stability of multiagent systems with time dependent communication links we study a simple but compelling model of network of agents interacting via time dependent communication links the model finds application in a variety of fields including synchronization swarming and distributed decision making in the model each agent updates his current state based upon the current information received from neighboring agents necessary and or sufficient conditions for the convergence of the individual agents states to a common value are presented thereby extending recent results reported in the literature the stability analysis is based upon a blend of graph theoretic and system theoretic tools with the notion of convexity playing a central role the analysis is integrated within a formal framework of set valued lyapunov theory which may be of independent interest among others it is observed that more communication does not necessarily lead to faster convergence and may eventually even lead to a loss of convergence even for the simple models discussed in the present paper

technical communique forced consensus in networks of double integrator systems with delayed input this communique presents forced second order consensus protocols with communication time delays for the network of agents with double integrator dynamics and gives a measure of the robustness of the protocols to the communication time delays by employing a frequency domain method it is proven that the forced consensus is achieved asymptotically for appropriate time delay if the network is connected particularly the maximum fixed time delay that can be tolerated by the network is found the forced consensus protocols are distributed in the sense that each agent only needs information from its neighboring agents which reduces the complexity of connections between agents significantly numerical simulation results are provided to demonstrate the effectiveness and the sharpness of the theoretical results

three and higher dimensional autonomous formations rigidity persistence and structural persistence in this paper we generalize the notion of persistence which has been originally introduced for two dimensional formations to r d for d 3 seeking to provide a theoretical framework for real world applications which often are in three dimensional space as opposed to the plane persistence captures the desirable property that a formation moves as a cohesive whole when certain agents maintain their distances from certain other agents we verify that many of the properties of rigid and or persistent formations established in r 2 are also valid for higher dimensions analysing the closed subgraphs and directed paths in persistent graphs we derive some further properties of persistent formations we also provide an easily checkable necessary condition for persistence we then turn our attention to consider some practical issues raised in multi agent formation control in three dimensional space we display a new phenomenon not present in r 2 whereby subsets of agents can behave in a problematic way when this behaviour is precluded we say that the graph depicting the multi agent formation has structural persistence in real deployment of controlled multi agent systems formations with underlying structurally persistent graphs are of interest we analyse the characteristics of structurally persistent graphs and provide a streamlined test for structural persistence we study the connections between the allocation of degrees of freedom dofs across agents and the characteristics of persistence and or structural persistence of a directed graph we also show how to transfer dofs among agents when the formation changes with new agent s added to preserve persistence and or structural persistence

gibbs sampler based coordination of autonomous swarms in this paper a novel gibbs sampler based algorithm is proposed for coordination of autonomous swarms the swarm is modeled as a markov random field mrf on a graph with a time varying neighborhood system determined by local interaction links the gibbs potential is designed to reflect global objectives and constraints it is established that with primarily local sensing communications the swarm configuration converges to the global minimizer s of the potential function the impact of the gibbs potential on the convergence speed is investigated finally a hybrid algorithm is developed to improve the efficiency of the stochastic scheme by integrating the gibbs sampler based method with the deterministic gradient flow method simulation results are presented to illustrate the proposed approach and verify the analyses

a remarkable periodic solution of the three body problem in the case of equal masses using a variational method we exhibit a surprisingly simple periodic orbit for the newtonian problem of three equal masses in the plane the orbit has zero angular momentum and a very rich symmetry pattern its most surprising feature is that the three bodies chase each other around a flxed eight shaped curve setting aside collinear motions the only other known motion along a flxed curve in the inertial plane is the lagrange relative equilibrium in which the three bodies form a rigid equilateral triangle which rotates at constant angular velocity within its circumscribing circle our orbit visits in turns every euler conflguration in which one of the bodies sits at the midpoint of the segment deflned by the other two figure 1 numerical computations

singular patterns for an aggregation model with a confining potential abstract we consider the aggregation equation with an attractive repulsive force law recent studies kolokolnikov et al 2011 22 von brecht et al 2012 23 balague et al 2013 15 have demonstrated that this system exhibits a very rich solution structure including steady states consisting of rings spots annuli n fold symmetries soccer ball patterns etc we show that many of these patterns can be understood as singular perturbations off lower dimensional equilibrium states for example an annulus is a bifurcation from a ring soccer ball patterns bifurcate off solutions that consist of delta point concentrations we apply asymptotic methods to classify the form and stability of many of these patterns to characterize spot solutions a class of semi linear aggregation problems is derived where the repulsion is described by a nonlinear term and the attraction is linear but non symmetric for a special class of perturbations that consists of a newtonian repulsion the spot shape is shown to be an ellipse whose precise dimensions are determined via a complex variable method for annular shapes their width and radial density profile are described using perturbation techniques

holotransformations of bacterial colonies and genome cybernetics we present a study of colony transformations during growth of bacillus subtilis under adverse environmental conditions it is a continuation of our pilot study of adaptive self organization during growth of bacterial colonies physica a 187 1992 378 first we identify and describe the transformations pathway i e the excitation of the branching modes from bacillus subtilis 168 grown under diffusion limited conditions and the phase transformations between the tip splitting phase phase t and the chiral phase phase c which belong to the same mode this pathway shows the evolution of complexity as the bacteria are exposed to adverse growth conditions we present the morphology diagram of phases t and c as a function of agar concentration and pepton level as expected the growth of phase t is ramified fractal like or dla like at low pepton level about 1 g 1 and turns compact at high pepton level about 10 g 1 the growth of phase c is also ramified at low pepton level and turns denser and finally compact as the pepton level increases generally speaking the colonies develop more complex patterns and higher micro level organization for more adverse environments we use the growth velocity as a response function to describe the growth at low agar concentration and low pepton level phase c grows faster than phase t and for a high agar concentration about 2 phase t grows faster we observe colony transformations between the two phases phase transformations they are found to be consistent with the fastest growing morphology selection principle adopted from azoic systems the transformations are always from the slower phase to the faster one hence we observe t c transformations at low agar concentrations and c t transformations at high agar concentrations we have observed both localized and extended transformations usually the transformations are localized for more adverse growth conditions and extended for growth conditions close to the boundaries between morphologies we have observed also transformations between different branching modes as well as transformations via virtual states motivated by the contemporary knowledge about phages and plasmids we postulate a theoretical framework to comply with our experimental findings we explain our observations using these assumptions as well as our proposal of co mutations and auto catalytic mutations as presented in the above mentioned pilot paper this theoretical framework is a part of the new evolving picture of genome cybernetics we also discuss the concept of adaptive genome changes which are based on pre existing knowledge as well as the concept of genetic learning i e changes in response to a new problem which develop the potential for adaptive genome changes these concepts follow naturally if the picture of genome cybernetics is accepted we conclude with a discussion of the implications and with further predictions to be tested experimentally derived from our assumptions

dynamic critical approach to self organized criticality a dynamic scaling ansatz for the approach to the self organized critical soc regime is proposed and tested by means of extensive simulations applied to the bak char21 sneppen model bs which exhibits robust soc behavior considering the short time scaling behavior of the density of sites ensuremath rho t below the critical value it is shown that i starting the dynamics with configurations such that ensuremath rho t 0 ensuremath rightarrow 0 one observes an initial increase of the density with exponent ensuremath theta 0 12 2 ii using initial configurations with ensuremath rho t 0 ensuremath rightarrow 1 the density decays with exponent ensuremath delta 0 47 2 it is also shown that the temporal autocorrelation decays with exponent c a 0 35 2 using these dynamically determined critical exponents and suitable scaling relationships all known exponents of the bs model can be obtained e g the dynamical exponent z 2 10 5 the mass dimension exponent d 2 42 5 and the exponent of all returns of the activity ensuremath tau text all 0 39 2 in excellent agreement with values already accepted and obtained within the soc regime

space dimension and scaling in fish school size distributions a simple model of aggregation has been used in its mean field version to explain the observed scaling property of tuna fish school size distributions bonabeau e and dagorn l 1995 phys rev e 51 5220 this model makes additional predictions when the dimension of the space in which the fish move is taken into account in this letter we identify two cases where the mean field assumption which was justified for free swimming tuna fish is no longer valid in these two examples scaling is also observed and the exponent is modified from the mean field case in a way predicted by the model

distributed consensus control for linear multi agent systems with discontinuous observations this article addresses the distributed consensus problem of linear multi agent systems with discontinuous observations over a time invariant undirected communication topology under the assumption that each agent can only intermittently share its outputs with the neighbours a class of distributed observer type of protocols are designed and utilised to achieve consensus by using appropriate matrix decomposition it is shown that consensus in the closed loop multi agent systems under a connected topology can be converted to the simultaneous asymptotic stability of a set of switching systems whose dimensions are the same as each agent from a multiple lyapunov functions approach it is proved that there exists a protocol to guarantee consensus if the communication time rate is larger than a threshold value furthermore a distributed pinning control method is employed to solve the consensus problem on an arbitrary given topology which needs not be connected particularly the questions of what kind of agen

non equilibrium dynamics of the ising model for t less than equal totc the growth of order in ising models with nonconserved order parameter is considered for quenches to final temperatures tf 0 and tf tc the results of numerical simulations in spatial dimension d 2 are presented in all cases a scaling regime is entered for sufficiently long times where the characteristic length scale is the domain size l t approximately t12 for tf 0 and the nonequilibrium correlation length xi t approximately t1z for tf tc the equal time correlation function has the expected scaling forms f r l t and r d 2 eta fc r xi t for tf 0 and tc respectively the scaling function fc x has interesting short distance behaviour which is elucidated using scaling arguments and by in and 1 n expansions the t 0 scaling function f x depends on whether the spin correlations present in the initial conditions are of long or short range as does the exponent which describes the decay of the autocorrelation function a t si t si o approximately l t results for a quench from the equilibrium critical state to tf 0 are consistent with theoretical predictions

on synchronous robotic networks part ii time complexity of rendezvous and deployment algorithms this paper analyzes a number of basic coordination algorithms running on synchronous robotic networks we provide upper and lower bounds on the time complexity of the move toward average and circumcenter laws both achieving rendezvous and of the centroid law achieving deployment over a region of interest the results are derived via novel analysis methods including a set of results on the convergence rates of linear dynamical systems defined by tridiagonal toeplitz and circulant matrices

discrete variational hamiltonian mechanics the main contribution of this paper is to present a canonical choice of a hamiltonian theory corresponding to the theory of discrete lagrangian mechanics we make use of lagrange duality and follow a path parallel to that used for construction of the pontryagin principle in optimal control theory we use duality results regarding sensitivity and separability to show the relationship between generating functions and symplectic integrators we also discuss connections to optimal control theory and numerical algorithms

diffusive influence systems influence systems seek to model how influence broadly defined spreads across a dynamic network we build a general analytical framework which we then use to prove that while turing complete influence dynamics of the diffusive type is almost surely asymptotically periodic in addition to resolving the dynamics of a widely used family of multiagent systems we introduce a general renormalization method for the bifurcation analysis of multiagent systems

state agreement for continuous time coupled nonlinear systems two related problems are treated in continuous time first the state agreement problem is studied for coupled nonlinear differential equations the vector fields can switch within a finite family associated to each vector field is a directed graph based in a natural way on the interaction structure of the subsystems generalizing the work of moreau under the assumption that the vector fields satisfy a certain subtangentiality condition it is proved that asymptotic state agreement is achieved if and only if the dynamic interaction digraph has the property of being sufficiently connected over time the proof uses nonsmooth analysis second the rendezvous problem for kinematic point mass mobile robots is studied when the robots fields of view have a fixed radius the circumcenter control law of ando e ieee trans robotics automation 15 1999 pp 818 828 is shown to solve the problem the rendezvous problem is a kind of state agreement problem but the interaction structure is state dependent

on the relation between vicsek and kuramoto models of spontaneous synchronization abstract the vicsek model for self propelling particles in 2d is investigated with respect to the addition of the stochastic perturbation of dynamic equations we show that this model represents in essence the same type of bifurcations under a different type of noise as the celebrated kuramoto model of spontaneous synchronization these models demonstrate similar behavior at least within the mean field approach to prove this we consider two types of noise for the vicsek model which are commonly considered in the literature the intrinsic and the extrinsic ones according to the terminology of pimentel et al j a pimentel m aldana c huepe h larralde intrinsic and extrinsic noise effects on phase transitions of network models with applications to swarming systems physical review e statistical nonlinear and soft matter physics 77 6 2008 doi 10 1103 physreve 77 061138 url http dx doi org 10 1103 physreve 77 061138 the qualitative correspondence with the bifurcation of stationary states in the kuramoto model is stated a new type of stochastic perturbation the mixed noise is proposed it is constructed as the weighted superposition of the intrinsic and the extrinsic noises the corresponding phase diagram noise amplitude vs interaction strength is obtained the possibility of the tricritical behavior for the vicsek model is predicted

a novel alignment repulsion algorithm for flocking of multi agent systems based on the number of neighbours per agent in this paper an energy based control methodology is proposed to satisfy the reynolds three rules in a flock of multiple agents first a control law is provided that is directly derived from the passivity theorem in the next step the number of neighbours alignment repulsion algorithm is introduced for a flock of agents which loses the cohesion ability and uniformly joint connectivity condition with this method each agent tries to follow the agents which escape its neighbourhood by considering the velocity of escape time and number of neighbours it is mathematically proved that the motion of multiple agents converges to a rigid and uncrowded flock if the group is jointly connected just for an instant moreover the conditions for collision avoidance are guaranteed during the entire process finally simulation results are presented to show the effectiveness of the proposed methodology

asynchronous variational integrators we describe a class of asynchronous variational integrators avi for nonlinear elastodynamics the avis are characterized by the following distinguishing attributes i the algorithms permit the selection of independent time steps in each element and the local time steps need not bear an integral relation to each other ii the algorithms derive from a spacetime form of a discrete version of hamilton s principle as a consequence of this variational structure the algorithms conserve local energy and momenta exactly subject to solvability of the local time steps numerical tests reveal that even when local energy balance is not enforced exactly the global and local energy behavior of the avis is quite remarkable a property which can probably be traced to the symplectic nature of the algorithm

state transitions and the continuum limit for a 2d interacting self propelled particle system we study a class of swarming problems wherein particles evolve dynamically via pairwise interaction potentials and a velocity selection mechanism we find that the swarming system undergoes various changes of state as a function of the self propulsion and interaction potential parameters in this paper we utilize a procedure which connects a class of individual based models to their continuum formulations and determine criteria for the validity of the latter h stability of the interaction potential plays a fundamental role in determining both the validity of the continuum approximation and the nature of the aggregation state transitions we perform a linear stability analysis of the continuum model and compare the results to the simulations of the individual based one c 2007 elsevier b v all rights reserved