emergent dynamics of winfree oscillators on locally coupled networks abstract the winfree model is the first mathematical model for synchronization of weakly coupled oscillators compared to the well known kuramoto model the winfree model does not conserve the total phase this leads to rich dynamic features compared to those produced by other phase models in this paper we study the emergent dynamics of the winfree model on a locally coupled static network a randomly chosen phase configuration undergoes several dynamic phase transitions such as incoherence partial locking complete locking partial oscillator death and complete oscillator death as the coupling strength increases we provide several rigorous analytical results on the emergence of these dynamic features we also provide several numerical simulations and compare their results to the analytical results

moving reproducing and dying beyond flatland malthusian flocks in dimensions d 2 we show that malthusian flocks i e coherently moving collections of self propelled entities such as living creatures which are being born and dying during their motion belong to a new universality class in spatial dimensions dg2 we calculate the universal exponents and scaling laws of this new universality class to o ensuremath epsilon in an ensuremath epsilon 4 ensuremath d expansion and find these are different from the canonical exponents previously conjectured to hold for immortal flocks i e those without birth and death and shown to hold for incompressible flocks in dg2 our expansion should be quite accurate in d 3 allowing precise quantitative comparisons between our theory simulations and experiments

an algorithmic approach to collective behavior the emergence of collective structure from the decentralized interaction of autonomous agents remains with notable exceptions a mystery while powerful tools from dynamics and statistical mechanics have been brought to bear sometimes with great success an algorithmic perspective has been lacking viewing collective behavior through the lens of natural algorithms offers potential benefits this article examines the merits and challenges of an algorithmic approach to the emergence of collective order

geometric decompositions of collective motion collective motion in nature is a captivating phenomenon revealing the underlying mechanisms which are of biological and theoretical interest will require empirical data modelling and analysis techniques here we contribute a geometric viewpoint yielding a novel method of analysing movement snapshots of collective motion are portrayed as tangent vectors on configuration space with length determined by the total kinetic energy using the geometry of fibre bundles and connections this portrait is split into orthogonal components each tangential to a lower dimensional manifold derived from configuration space the resulting decomposition when interleaved with classical shape space construction is categorized into a family of kinematic modes including rigid translations rigid rotations inertia tensor transformations expansions and compressions snapshots of empirical data from natural collectives can be allocated to these modes and weighted by fractions of total kinetic energy such quantitative measures can provide insight into the variation of the driving goals of a collective as illustrated by applying these methods to a publicly available dataset of pigeon flocking the geometric framework may also be profitably employed in the control of artificial systems of interacting agents such as robots

painleve equations nonlinear special functions the six painleve equations pi pvi were first discovered about a hundred years ago by painleve and his colleagues in an investigation of nonlinear second order ordinary differential equations recently there has been considerable interest in the painleve equations primarily due to the fact that they arise as reductions of the soliton equations which are solvable by inverse scattering consequently the painleve equations can be regarded as completely integrable equations and possess solutions which can be expressed in terms of solutions of linear integral equations despite being nonlinear equations although first discovered from strictly mathematical considerations the painleve equations have arisen in a variety of important physical applications including statistical mechanics plasma physics nonlinear waves quantum gravity quantum field theory general relativity nonlinear optics and fibre optics the painleve equations may be thought of a nonlinear analogues of the classical special functions they possess hierarchies of rational solutions and one parameter families of solutions expressible in terms of the classical special functions for special values of the parameters further the painleve equations admit symmetries under affine weyl groups which are related to the associated backlund transformations in this paper i discuss some of the remarkable properties which the painleve equations possess including connection formulae backlund transformations associated discrete equations and hierarchies of exact solutions in particular the second painleve equation pii is used to illustrate these properties and some of the applications of pii are also discussed

on the general consensus protocol of multi agent systems with double integrator dynamics in this paper a general consensus protocol is considered for multi agent systems with double integrator dynamics the advantage of this protocol is that different consensus dynamics including linear periodic and positive exponential dynamics can be realized by choosing different gains necessary and sufficient conditions for solving the consensus problem with the considered general protocol are obtained namely all the gains realizing the consensus can be described the design method of the consensus protocol is constructively given moreover a periodic consensus protocol is obtained as a special case and it is revealed that the maximum convergence speed can be achieved by choosing suitable gains

conjectures of alperin and broue for 2 blocks with elementary abelian defect groups of order 8 using the classification of finite simple groups we prove alperin s weight conjecture and the character theoretic version of broue s abelian defect group conjecture for 2 blocks of finite groups with an elementary abelian defect group of order 8

existence of piecewise weak solutions of a discrete cucker smale s flocking model with a singular communication weight abstract we prove existence of global c 1 piecewise weak solutions for the discrete cucker smale s flocking model with a non lipschitz communication weight s s 0 1 we also discuss the possibility of finite in time alignment of the velocities of the particles

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

gaslike model of social motility we propose a model to represent the motility of social elements the model is completely deterministic possesses a small number of parameters and exhibits a series of properties that are reminiscent of the behavior of comunities in social ecological competition these are i similar individuals attract each other ii individuals can form stable groups iii a group of similar individuals breaks into subgroups if it reaches a critical size iv interaction between groups can modify the distribution of the elements as a result of fusion fission or pursuit v individuals can change their internal state by interaction with their neighbors the simplicity of the model and its richness of emergent behaviors such as for example pursuit between groups make it a useful toy model to explore a diversity of situations by changing the rule by which the internal state of individuals is modified by the interactions with the environment

supercritical analysis of strongly nonlinear vortices in magnetized ferrofluids the structure of two dimensional vortices in a thin layer of magnetized ferrofluid heated from above is examined in the limit as the critical wavenumber a of the roll cells becomes large in particular we present a nonlinear asymptotic description of the vortex pattern that occurs directly above the critical point in parameter space where instability first sets in two cases are examined first an idealized case where the fluid layer has boundary conditions appropriate for a free surface and second a more physical situation where the fluid is confined between rigid horizontal magnetic pole pieces the idealized problem has a relatively simple solution structure which is a leading order approximation to the solution of the physical problem as the critical wavenumber increases boundary layers of thickness o a 4 3 develop at the walls in the physical problem and the critical value of the instability parameter has an asymptotic expansion in inverse powers of a 2 weakly nonlinear solutions are extended into the unstable region of parameter space where the convection is described by fully nonlinear equations and the perturbations to the basic state have finite amplitude this analysis is new since similar large wavenumber investigations in other problems do not apply at critical conditions as the instability parameter is increased above its critical value a hierarchy of bifurcations in the equations governing the temperature perturbation occurs necessitating the inclusion of progressively more harmonics in the solution numerical solutions for the first few of these temperature equations are presented and asymptotic expressions for the heat transfer across the fluid layer for both sets of boundary conditions are derived although the conduction state still dominates the heat transfer the solution structure is fundamentally different from previous weakly nonlinear theories finally some numerical solutions of the full steady state governing equations are presented and compared with the asymptotic structures these results verify that the solutions obtained with both sets of boundary conditions are asymptotic to one another in the large wavenumber limit and that the asymptotic solution is a useful approximation in this limit

self organized hydrodynamics with congestion and path formation in crowds a continuum model for self organized dynamics is numerically investigated the model describes systems of particles subject to alignment interaction and short range repulsion it consists of a non conservative hyperbolic system for the density and velocity orientation short range repulsion is included through a singular pressure which becomes infinite at the jamming density the singular limit of infinite pressure stiffness leads to phase transitions from compressible to incompressible dynamics the paper proposes an asymptotic preserving scheme which takes care of the singular pressure while preventing the breakdown of the courant friedrichs lewy cfl stability condition near congestion it relies on a relaxation approximation of the system and an elliptic formulation of the pressure equation numerical simulations of impinging clusters show the efficiency of the scheme to treat congestions a two fluid variant of the model provides a model of path formation in crowds

spectral method for a kinetic swarming model in this paper we present the first numerical method for a kinetic description of the vicsek swarming model the kinetic model poses a unique challenge as there is a distribution dependent collision invariant to satisfy when computing the interaction term we use a spectral representation linked with a discrete constrained optimization to compute these interactions to test the numerical scheme we investigate the kinetic model at different scales and compare the solution with the microscopic and macroscopic descriptions of the vicsek model we observe that the kinetic model captures key features such as vortex formation and traveling waves

donovan s conjecture blocks with abelian defect groups and discrete valuation rings we give a reduction to quasisimple groups for donovan s conjecture for blocks with abelian defect groups defined with respect to a suitable discrete valuation ring mathcal o consequences are that donovan s conjecture holds for mathcal o blocks with abelian defect groups for the prime two and that using recent work of farrell and kessar for arbitrary primes donovan s conjecture for mathcal o blocks with abelian defect groups reduces to bounding the cartan invariants of blocks of quasisimple groups in terms of the defect a result of independent interest is that in general i e for arbitrary defect groups donovan s conjecture for mathcal o blocks is a consequence of conjectures predicting bounds on the mathcal o frobenius number and on the cartan invariants as was proved by kessar for blocks defined over an algebraically closed field

quantitative assessment of the toner and tu theory of polar flocks we present a quantitative assessment of the toner and tu theory describing the universal scaling of fluctuations in polar phases of dry active matter using large scale simulations of the vicsek model in two and three dimensions we find the overall phenomenology and generic algebraic scaling predicted by toner and tu but our data on density correlations reveal some qualitative discrepancies the values of the associated scaling exponents we estimate differ significantly from those conjectured in 1995 in particular we identify a large crossover scale beyond which flocks are only weakly anisotropic we discuss the meaning and consequences of these results

consensus in a heterogeneous influence network we consider a dynamical network model in which a number of agents all move on the plane with the same constant absolute velocity at each time step each agent s direction is updated as the average of its direction plus the directions of other agents who can influence it the influencing capability of each agent is represented by its influencing radius which is randomly chosen according to a power law distribution with a scaling exponent between 2 and ensuremath infty as the value of the scaling exponent decreases the radius distribution becomes more heterogeneous and the network becomes much easier to achieve direction consensus among agents due to the leading roles played by a few hub agents furthermore almost all agents will finally move in the same desired direction in a strong heterogeneous influence network if and only if a small fraction of hub agents can be controlled to move in the desired direction these results also reflect the robust yet fragile feature of a heterogeneous influence network

a new class of finite time nonlinear consensus protocols for multi agent systems this paper is devoted to investigating the finite time consensus problem for a multi agent system in networks with undirected topology a new class of global continuous time invariant consensus protocols is constructed for each single integrator agent dynamics with the aid of lyapunov functions in particular it is shown that the settling time of the proposed new class of finite time consensus protocols is upper bounded for arbitrary initial conditions this makes it possible for network consensus problems that the convergence time is designed and estimated offline for a given undirected information flow and a group volume of agents finally a numerical simulation example is presented as a proof of concept

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

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

average consensus in networks of dynamic agents with switching topologies and multiple time varying delays in this paper we discuss average consensus problem in undirected networks of dynamic agents with fixed and switching topologies as well as multiple time varying communication delays by employing a linear matrix inequality method we prove that all the nodes in the network achieve average consensus asymptotically for appropriate communication delays if the network topology is connected particularly several feasible linear matrix inequalities are established to determine the maximal allowable upper bound of time varying communication delays numerical examples are given to demonstrate the effectiveness and the sharpness of the theoretical results

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

critical and oscillatory behavior of a system of smart preys and predators it is shown that a system of smart preys and predators exhibits irreversible phase transitions between a regime of prey predator coexistence and an state where predator extinction is observed within the coexistence regime the system exhibits a transition between a regime where the densities of species remain constant and another with self sustained oscillations respectively this transition is located by means of a combined treatment involving finite size scaling and fourier transforms furthermore it is shown that the transition can be rationalized in terms of the standard percolation theory the existence of an oscillatory regime in the thermodynamic limit which is in contrast to previous findings of boccara et al phys rev e 50 4531 1994 may be due to subtle differences between the studied models

on donovan s conjecture abstract this article contains reduction theorems for some weaker variants of donovan s conjecture which supposes that for every finite group d of prime order p there are only finitely many morita equivalence classes of p blocks of finite groups having defect groups isomorphic to d i when restricting the conjecture to the case of abelian defect groups it can be reduced to only considering p blocks of a class of groups that are close to being direct products of simple groups ii when restricting the conjecture to the case of principal blocks of finite groups having an abelian sylow p subgroup it can be reduced to only considering p blocks of simple groups a weaker version of donovan s conjecture would suppose that there are only finitely many cartan matrices of p blocks of finite groups with defect group isomorphic to a given one iii this conjecture can be reduced to only considering p blocks of quasisimple groups with centers having orders prime to p

d alembert s paradox since classical inviscid theory leads to the patently absurd conclusion that the resistance experienced by a rigid body moving through a fluid with uniform velocity is zero great efforts have been made during the last hundred or so years to propose alternate theories and to explain how a vanishingly small frictional force in the fluid can nevertheless have a significant effect on the flow properties the methods used are a combination of experimental observation computation often on a very large scale and analysis of the structure of the asymptotic form of the solution as the friction tends to zero this three pronged attack has achieved considerable success especially during the last ten years so that now the paradox may be regarded as largely resolved the lecture will review these achievements in subsonic and supersonic flow for bluff bodies for trailing edge flows and for internal flows most of the work has been on steady two dimensional problems but the special difficulties in unsteady and th

on consensus speed of multi agent systems with double integrator dynamics the performance of multi agent systems is an important issue in this paper it is focused on consensus speed for multi agent systems with double integrator dynamics and fixed undirected graphes under a kind of consensus protocols it is revealed that under some conditions the maximum consensus speed is determined by the largest and the smallest nonzero eigenvalues of the laplacian matrix of the undirected connected graph based on the mentioned results arbitrary desired consensus speed can be achieved by choosing suitable feedback gains numerical simulations are given to illustrate the main results

a local sensitivity analysis for the hydrodynamic cucker smale model with random inputs abstract we present a local sensitivity analysis for the hydrodynamic cucker smale hcs model with random inputs in the absence of random inputs the hcs model was derived as a macroscopic model for the emergent dynamics of the cs flocking ensemble from the kinetic cs model via the moment method and mono kinetic ansatz for a closure condition in this paper we incorporate the uncertain effects together with the hcs model to result in the random hcs model for definiteness we consider the uncertainties in initial data and communication weight function for this random hcs model we perform local sensitivity estimates such as the propagation of pathwise well posedness pathwise l 2 stability and flocking estimates of solution process

emergent behavior of a cucker smale type particle model with nonlinear velocity couplings in this note we present a cucker smale type flocking model with nonlinear velocity couplings and derive sufficient conditions for the formation of flocking in terms of communication weight and initial spatial velocity standard deviations

asymptotic properties of consensus type algorithms for networked systems with regime switching topologies this paper is concerned with asymptotic properties of consensus type algorithms for networked systems whose topologies switch randomly the regime switching process is modeled as a discrete time markov chain with a finite state space the consensus control is achieved by using stochastic approximation methods in the setup the regime switching process the markov chain contains a rate parameter e 0 in the transition probability matrix that characterizes how frequently the topology switches on the other hand the consensus control algorithm uses a stepsize m that defines how fast the network states are updated depending on their relative values three distinct scenarios emerge under suitable conditions we show that when 0 e o m a continuous time interpolation of the iterates converges weakly to a system of randomly switching ordinary differential equations modulated by a continuous time markov chain in this case a scaled sequence of tracking errors converges to a system of switching diffusion when 0 email protected email protected the network topology is almost non switching during consensus control transient intervals and hence the limit dynamic system is simply an autonomous differential equation when email protected email protected the markov chain acts as a fast varying noise and only its averaged network matrices are relevant resulting in a limit differential equation that is an average with respect to the stationary measure of the markov chain simulation results are presented to demonstrate these findings

blocks inequivalent to their frobenius twists abstract let k be an algebraically closed field of characteristic p we give a general method for producing examples of blocks b of finite group algebras that are not morita equivalent as k algebras to the frobenius twist b p our method produces non nilpotent blocks having one simple module and elementary abelian defect group these also provide the first known examples of blocks where there is a perfect isotypy at the level of ordinary characters with all the signs positive but no derived equivalence between the blocks we do not know of any examples of blocks b that are not morita equivalent to the second frobenius twist b p 2

stability of nonlinear regime switching jump diffusion abstract motivated by networked systems stochastic control optimization and a wide variety of applications this work is devoted to systems of switching jump diffusions treating such nonlinear systems we focus on stability issues one of the distinct features considered here is that the switching process depends on the jump diffusions first asymptotic stability in the large is obtained then the study on exponential p stability is carried out connection between almost surely exponential stability and exponential p stability is exploited also presented are smooth dependence on the initial data using the smooth dependence necessary conditions for exponential p stability are derived then criteria for asymptotic stability in distribution are provided a couple of examples are given to illustrate our results

consensus analysis of switching multi agent systems with fixed topology and time delay abstract this paper investigates the average consensus problems of the discrete time markov switching linear multi agent systems lmas with fixed topology and time delay firstly we introduce a concept of the average consensus to adapt the stochastic systems secondly a time delay switching consensus protocol is proposed by developing a new signal mode the switching signal of the systems and the time delay signal of the controller can be merged into one signal thirdly by lyapunov technique two lmis criteria of average consensus are provided and they reveal that the consensus of the multi agent systems relates to the spectral radius of the laplacian matrix furthermore by our results and ccl type algorithms we can get the gain matrices finally a numerical example is given to illustrate the efficiency of our results

from discrete cucker smale model to continuous cucker smale model in a temperature field we study emergent dynamics of the discrete and continuous cucker smale c s models in a self consistent temperature field and provide refined monocluster flocking estimates more precisely we present a sufficient framework leading to the monocluster flocking toward the constant common temperature and velocity exponentially fast this improves the authors earlier work where existence of common temperature and velocity are not identified our proposed sufficient framework is formulated in terms of the initial data and system parameters using the refined flocking we also provide a uniform in time convergence from the discrete model to the continuous model under some suitable compatibility condition on the asymptotic velocities for the discrete and continuous model as the time step tends to zero we also provide several numerical examples and compare them with analytical results we study emergent dynamics of the discrete and continuous cucker smale c s models in a self consistent temperature field and provide refined monocluster flocking estimates more precisely we present a sufficient framework leading to the monocluster flocking toward the constant common temperature and velocity exponentially fast this improves the authors earlier work where existence of common temperature and velocity are not identified our proposed sufficient framework is formulated in terms of the initial data and system parameters using the refined flocking we also provide a uniform in time convergence from the discrete model to the continuous model under some suitable compatibility condition on the asymptotic velocities for the discrete and continuous model as the time step tends to zero we also provide several numerical examples and compare them with analytical results

towards donovan s conjecture for abelian defect groups abstract we define a new invariant for a p block of a finite group the strong frobenius number which we use to address the problem of reducing donovan s conjecture to normal subgroups of index p as an application we use the strong frobenius number to complete the proof of donovan s conjecture for 2 blocks with abelian defect groups of rank at most 4 and for 2 blocks with abelian defect groups of order at most 64

the structure of blocks with a klein four defect group we prove erdmann s conjecture stating that every block with a klein four defect group has a simple module with trivial source and deduce from this that puig s finiteness conjecture holds for source algebras of blocks with a klein four defect group the proof uses the classification of finite simple groups

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

exit dynamics of occupant evacuation in an emergency abstract a two dimensional cellular automata model is proposed to simulate the exit dynamics of occupant evacuation concerning the exit width and the door separation we put forward some useful standpoints 1 exit width should be bigger than a critical value and the door separation should be neither too small nor too big 2 for single exit door with the increase of exit width the flux per unit width will decrease but the total flux will always increase 3 the total flux of the exit is an increasing nonlinear function of the exit width 4 the optimal value of the door separation does not vary with the value of exit width 5 the layout of exits should be symmetry those results are helpful in performance based design of building

2 blocks with abelian defect groups we give a classification up to morita equivalence of 2 blocks of quasi simple groups with abelian defect groups as a consequence we show that donovan s conjecture holds for elementary abelian 2 groups and that the entries of the cartan matrices are bounded in terms of the defect for arbitrary abelian 2 groups we also show that a block with defect groups of the form c2m c2m for m 2 has one of two morita equivalence types and hence is morita equivalent to the brauer correspondent block of the normaliser of a defect group this completes the analysis of the morita equivalence types of 2 blocks with abelian defect groups of rank 2 from which we conclude that donovan s conjecture holds for such 2 groups a further application is the completion of the determination of the number of irreducible characters in a block with abelian defect groups of order 16 the proof uses the classification of finite simple groups

existence properties and trajectory specification of generalised multi agent flocking a class of flocking algorithms for second order multi agent networks with single virtual leaders are developed by including more weighting and navigating matrices in this paper flocking existence

equilibria and steering laws for planar formations abstract this paper presents a lie group setting for the problem of control of formations as a natural outcome of the analysis of a planar two vehicle formation control law the vehicle trajectories are described using the planar frenet serret equations of motion which capture the evolution of both the vehicle position and orientation for unit speed motion subject to curvature steering control the set of all possible relative equilibria for arbitrary g invariant curvature controls is described where g se 2 is a symmetry group for the control law and a global convergence result for the two vehicle control law is proved an n vehicle generalization of the two vehicle control law is also presented and the corresponding relative equilibria for the n vehicle problem are characterized work is on going to discover stability and convergence results for the n vehicle problem

styled velocity flocking of autonomous vehicles a systematic design this paper develops a measure theoretic approach for generating the collective behavior of flocking of planar autonomous vehicles under all to all communication scheme to obtain flocking protocol we formulate the notion of state of styled velocity flocking for the target state of a design problem instead of considering solution ansatzes this notion captures a broader class of flocking behaviors of non parallel motions as well as embodies the two important performances of cohesion maintenance and collision avoidance to pose a control design problem a measure valued transition equation is obtained to induce an auxiliary one body continuum model from the exact multi body particle model of the collective system the design problem is then formulated on the auxiliary continuum model and a systematic design procedure is presented the state of styled velocity flocking of the particle model under the obtained flocking protocol is then verified with an important result on the continuous dependence on initial data of solutions of the measured valued transition equation application to elliptical flocking of mobile robots is presented to illustrate the novelty of the presented theory

short range interactions versus long range correlations in bird flocks bird flocks are a paradigmatic example of collective motion one of the prominent traits of flocking is the presence of long range velocity correlations between individuals which allow them to influence each other over the large scales keeping a high level of group coordination a crucial question is to understand what is the mutual interaction between birds generating such nontrivial correlations here we use the maximum entropy me approach to infer from experimental data of natural flocks the effective interactions between individuals compared to previous studies we make a significant step forward as we retrieve the full functional dependence of the interaction on distance and find that it decays exponentially over a range of a few individuals the fact that me gives a short range interaction even though its experimental input is the long range correlation function shows that the method is able to discriminate the relevant information encoded in such correlations and single out a minimal number of effective parameters finally we show how the method can be used to capture the degree of anisotropy of mutual interactions

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

consensus of second order multi agent systems with delayed nonlinear dynamics and intermittent communications this article investigates the second order consensus problem of multi agent systems with inherent delayed nonlinear dynamics and intermittent communications each agent is assumed to obtain the measurements of relative states between its own and the neighbours only at a sequence of disconnected time intervals a new kind of protocol based only on the intermittent measurements of neighbouring agents is proposed to guarantee the states of agents to reach second order consensus under a fixed strongly connected and balanced topology by constructing a common lyapunov function it is shown that consensus can be reached if the general algebraic connectivity and communication time duration are larger than their corresponding threshold values respectively finally simulation examples are provided to verify the effectiveness of the theoretical analysis

optimal control of discrete time fractional multi agent systems abstract this paper deals with control strategies for discrete time fractional multi agent systems by using the discrete fractional order operator we introduce memory effects to the considered problem necessary optimality conditions for discrete time fractional optimal control problems with single and double summator dynamics are proved and simulation results are presented

large wavenumber vortices in time periodic flows the linear stability properties of short wavelength vortices within time periodic flows are examined using a wkb based asymptotic analysis such vortices typically have an instantaneous growth rate considerably larger than the time scale of the underlying flow and thus have often been studied using quasi steady techniques a major drawback of these quasi steady approaches is that although they are able to determine the instantaneous flow structure they are of no use in describing the evolution of the modes it is shown how rational asymptotic analysis based on wkb ideas overcomes this deficiency and enables the form of the neutral stability curve to be obtained for short wavelengths the technique is applied to three problems first the key features of the analysis are exemplified by careful consideration of a model problem which is motivated by the physical situation of the sinusoidal heating of a horizontal flat plate bounding a semi infinite layer of fluid the governing linearized stability equations take the form of a system which is sixth order in the spatial variable and second order in time however the important features of this system are captured by our model which is only second order in the spatial coordinate and first order in time the second physically important flow examined is the motion induced in a viscous fluid surrounding a long torsionally oscillating cylinder a curved stokes flow detailed asymptotic and numerical studies of both the model and the two physically motivated flows are undertaken and it is shown how the analytical results provide good qualitative agreement with the numerical findings at quite modest wavenumbers the methodology adopted here may be used as a basis for the rational study of the stability properties of other time periodic flows a key result forthcoming from this study is the demonstration that the first few terms in the relevant high wavenumber form of the neutral curve for modes in an oscillatory flow may be derived relatively quickly with minimal computational effort

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

numerical analysis of behaviour of the cucker smale type models with fractional operators abstract the behaviour of fractional order multi agent discrete time systems is examined by numerical analysis we consider the cucker smale type models with fractional operators the asymptotic stability of a class of linear fractional discrete time systems as a tool providing a consensus in the nonlinear fractional discrete time systems is investigated the proposed results are based on linearization method of the considered multi agent system interesting examples illustrate the effectiveness of the derived results

state estimation of heterogeneous oscillators by means of proximity measurements in this paper we aim at estimating the state of an ensemble of mobile agents specifically each agent is an oscillator which moves along a circle at a given time varying angular velocity we assume that an agent can measure the distance from the other oscillators only when they are in its proximity we propose a recursive algorithm which based on these intermittent and uncertain measurements is capable of estimating in real time the relative angular position of the agents the algorithm combines the information coming from the collected measures with the information on the agents dynamics and its convergence is proved by means of interval analysis the theoretical analysis is complemented with extensive numerical simulations

singular perturbation analysis of a reduced model for collective motion a renormalization group approach in a system of noisy self propelled particles with interactions that favor directional alignment collective motion will appear if the density of particles is beyond a critical density starting with a reduced model for collective motion we determine how the critical density depends on the form of the initial perturbation specifically we employ a renormalization group improved perturbative method to analyze the model equations and show analytically up to first order in the perturbation parameter how the critical density is modified by the strength of the initial angular perturbation in the system

refined blowup criteria and nonsymmetric blowup of an aggregation equation abstract we consider an aggregation equation in r d d 2 with fractional dissipation u t u k u u where 0 0 1 and k x e x we prove a refined blowup criteria by which the global existence of solutions is controlled by its l x q norm for any d d 1 q we prove the finite time blowup of solutions for a general class of nonsymmetric initial data the argument presented works for both the inviscid case 0 and the supercritical case 0 and 0 1 additionally we present new proofs of blowup which does not use free energy arguments

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

force estimation and prediction from time varying density images we present methods for estimating forces which drive motion observed in density image sequences using these forces we also present methods for predicting velocity and density evolution to do this we formulate and apply a minimum energy flow mef method which is capable of estimating both incompressible and compressible flows from time varying density images both the mef and force estimation techniques are applied to experimentally obtained density images spanning spatial scales from micrometers to several kilometers using density image sequences describing cell splitting for example we show that cell division is driven by gradients in apparent pressure within a cell using density image sequences of fish shoals we also quantify 1 intershoal dynamics such as coalescence of fish groups over tens of kilometers 2 fish mass flow between different parts of a large shoal and 3 the stresses acting on large fish shoals

a local sensitivity analysis for the kinetic cucker smale equation with random inputs abstract we present a local sensitivity analysis for the kinetic cucker smale c s equation with random inputs this is a companion work to our previous local sensitivity analysis for the particle c s model random inputs in the coefficients of the kinetic c s equation can be caused by diverse sources such as the incomplete measurement and interactions with unknown environments and will enter the problem through the communication function or initial data for the proposed random kinetic c s equation we present sufficient conditions for the pathwise well posedness and flocking estimates for the local sensitivity analysis we study the propagation of regularity of the kinetic density function in random space

study of interacting particle systems the transition to the oscillatory behavior of a prey predator model abstract a prey predator system with intelligent pursuit and evasion is studied by means of computer simulations it is found that the model exhibits a coexistence state between prey and predators in this state and depending on the parameters the system may evolve toward two different regimes characterized by the behavior of the prey predator population whitin the oscillatory fixed point regime the specie s density changes periodically remains constant respectively the transition between such regimes is rationalized in terms of a dynamic percolation process

the structure of highly nonlinear vortices in curved channel flow the structure of highly nonlinear small wavelength gortler vortices is analysed for fully developed flow in a curved channel the taylor number is taken to be t 0 epsilon 5 which is asymptotically larger than the neutral stability taylor number for vortices of small wavelength 2 pi epsilon over most of the flow domain the motion is determined by the interaction of the mean flow and terms proportional to exp iz epsilon whereas adjacent to the outer channel wall there is a boundary layer of thickness o epsilon which requires all the harmonics of the disturbance to be considered numerical solutions of the wall layer equations are presented for t 0 up to 14 000 with the main feature of these results being the development of a weak vortex on the boundary layer lengthscale

complete classification of the asymptotical behavior for singular c s model on the real line abstract in this paper we study the singular cucker smale c s model on the real line for long range case i e 1 we prove the uniqueness of the solution in the sense of definition 2 1 and the unconditional flocking emergence moreover the sufficient and necessary condition for collision and sticking phenomenon will be provided for short range case i e 1 we construct the uniform in time lower bound of the relative distance between particles and provide the sufficient and necessary condition for the emergence of multi cluster formation for critical case i e 1 we show the uniform lower bound of the relative distance and unconditional flocking emergence these results provide a complete classification of the collective behavior for c s model on the real line

swarming patterns in a two dimensional kinematic model for biological groups we construct a continuum model for the motion of biological organisms experiencing social interactions and study its pattern forming behavior the model takes the form of a conservation law in two spatial dimensions the social interactions are modeled in the velocity term which is nonlocal in the population density and includes a parameter that controls the interaction length scale the dynamics of the resulting partial integrodifferential equation may be uniquely decomposed into incompressible motion and potential motion for the purely incompressible case the model resembles one for fluid dynamical vortex patches there exist solutions which have constant population density and compact support for all time numerical simulations produce rotating structures which have circular cores and spiral arms and are reminiscent of naturally observed phenomena such as ant mills the sign of the social interaction term determines the direction of the rotation and the interaction length scale affects the degree o

continuum modeling of the equilibrium and stability of animal flocks abstract groups of animals often tend to arrange themselves in flocks that have characteristic spatial attributes and temporal dynamics using a dynamic continuum model for a flock of individuals we find equilibria of finite spatial extent where the density goes continuously to zero at a well defined flock edge and we discuss conditions on the model that allow for such solutions we also demonstrate conditions under which as the flock size increases the interior density in our equilibria tends to an approximately uniform value motivated by observations of starling flocks that are relatively thin in a direction transverse to the direction of flight we investigate the stability of infinite planar sheet flock equilibria we find that long wavelength perturbations along the sheet are unstable for the class of models that we investigate this has the conjectured consequence that sheet like flocks of arbitrarily large transverse extent relative to their thickness do not occur however we also show that our model admits approximately sheet like pancake shaped three dimensional ellipsoidal equilibria with definite aspect ratios transverse length scale to flock thickness determined by anisotropic perceptual response characteristics of the flocking individuals and we argue that these pancake like equilibria are stable to the previously mentioned sheet instability

statistical mechanics for natural flocks of birds flocking is a typical example of emergent collective behavior where interactions between individuals produce collective patterns on the large scale here we show how a quantitative microscopic theory for directional ordering in a flock can be derived directly from field data we construct the minimally structured maximum entropy model consistent with experimental correlations in large flocks of starlings the maximum entropy model shows that local pairwise interactions between birds are sufficient to correctly predict the propagation of order throughout entire flocks of starlings with no free parameters we also find that the number of interacting neighbors is independent of flock density confirming that interactions are ruled by topological rather than metric distance finally by comparing flocks of different sizes the model correctly accounts for the observed scale invariance of long range correlations among the fluctuations in flight direction

the fully nonlinear development of gortler vortices in growing boundary layers the fully nonlinear development of small wavelength gortler vortices in a growing boundary layer is investigated by a combination of asymptotic and numerical methods the starting point for the analysis is the weakly nonlinear theory of hall j inst math applies 29 173 1982 who discussed the initial development of large wavenumber small amplitude vortices in a neighbourhood of the location where they first become linearly unstable that development is unusual in the context of nonlinear stability theory in that it is not described by the stuart watson approach in fact the development is governed by a pair of coupled nonlinear partial differential evolution equations for the vortex flow and the mean flow correction here the further development of this interaction is considered for vortices so large that the mean flow correction driven by them is as large as the basic state surprisingly it is found that such a nonlinear interaction can still be described by asymptotic means it is shown that the vortices spread out across the boundary layer and effectively drive the boundary layer in fact the system obtained by the equations for the fundamental component of the vortex generates a differential equation for the basic state thus the mean flow adjusts so as to make these large amplitude vortices locally neutral moreover in the region where the vortices exist the mean flow has a square root profile and the vortex velocity field can be written down in closed form the upper and lower boundaries of the region of vortex activity are determined by a free boundary problem involving the boundary layer equations in general it is found that this region ultimately includes almost all of the original boundary layer and much of the free stream in this situation the mean flow has essentially no relation to the flow that exists in the absence of the vortices