a borderline random fourier series consider a mean zero random variable x and an independent sequence x n distributed like x we show that the random fourier series n 1 n 1 x n exp 2i nt converges uniformly almost surely if and only if e x log log max e e x

synchronization in general complex dynamical networks with coupling delays abstract complex networks have attracted increasing attention from various fields of science and engineering today due to the finite speeds of transmission and spreading as well as traffic congestions a signal or influence travelling through a complex network often is associated with time delays and this is very common in biological and physical networks in this paper we introduce complex dynamical network models with coupling delays for both continuous and discrete time cases and then investigate their synchronization phenomena and criteria based on these new complex network models we derive synchronization conditions for both delay independent and delay dependent asymptotical stabilities in terms of linear matrix inequalities lmi we finally use a network with a fixed delay and a specific coupling scheme as an example to illustrate the theoretical results

zero lag synchronization and multiple time delays in two coupled chaotic systems zero lag synchronization zls between two chaotic systems coupled by a portion of their signal is achieved for restricted ratios between the delays of the self feedback and the mutual coupling we extend this scenario to the case of a set of multiple self feedbacks n d i and a set of multiple mutual couplings n c j we demonstrate both analytically and numerically that zls can be achieved when ensuremath sum l i n d i ensuremath sum m j n c j 0 where l i m j mathbb z results which were mainly derived for bernoulli maps and exemplified with simulations of the lang kobayashi differential equations indicate that zls can be achieved for a continuous range of mutual coupling delay this phenomenon has an important implication in the possible use of zls in communication networks

opinion dynamics of modified hegselmann krause model in a group based population with heterogeneous bounded confidence abstract continuous opinion dynamics in a group based population with heterogeneous bounded confidences is considered in this paper a slightly modified hegselmann krause model is proposed and agents are classified into three categories open minded moderate minded and closed minded agents while the whole population is divided into three subgroups accordingly we study how agents of each category and the population size can affect opinion dynamics it is observed that the number of final opinion clusters is dominated by the closed minded agents open minded agents cannot contribute to forming opinion consensus and the existence of open minded agents may diversify the final opinions instead for the fixed population size and proportion of closed minded agents the relative size of the largest final opinion cluster varies along concave parabola like curve as the proportion of open minded agents increases and there is a tipping point when the number of open minded agents is almost equal to that of moderate minded agents for the fixed proportion of the three categories in the population as the population size becomes larger the number of final opinion clusters will reach a plateau some of the results are different from the previous studies

multi objective retrospective optimization using stochastic zigzag search abstract we propose a new retrospective optimization ro method for multi objective simulation optimization moso problems ro algorithms generate a sequence of sample path sp problems and solve these sp problems iteratively using a nonlinear optimizer in this study a stochastic zigzag search algorithm is chosen in the ro framework to solve sp problems the key idea of zigzag search is searching around the pareto front by applying an efficient local search procedure using the gradients of the objective functions many continuous moso problems have smooth objective functions and their non dominated objective function values form a smooth surface in the image space this fact motivates developing the zigzag search method embedded in ro for such relatively well posed moso problems a numerical implementation of this method multi objective retrospective optimization using zigzag search morozs is presented particularly for continuous bi objective simulation optimization boso problems with well connected pareto optimal solutions morozs is designed for boso problems in which a simulation oracle returns both objective function values and gradients due to the local nature of zigzag search morozs can only guarantee the asymptotic convergence to local pareto optimality the efficiency of morozs is studied using three boso problems with noisy objective functions and is compared to that of genetic algorithms based nsga ii and a recently developed method mo compass

opinion dynamics in heterogeneous networks convergence conjectures and theorems recently significant attention has been dedicated to the models of opinion dynamics in which opinions are described by real numbers and agents update their opinions synchronously by averaging their neighbors opinions the neighbors of each agent can be defined as either 1 those agents whose opinions are in its confidence range or 2 those agents whose influence range contain the agent s opinion the former definition is employed in hegselmann and krause s bounded confidence model and the latter is novel here as the confidence and influence ranges are distinct for each agent the heterogeneous state dependent interconnection topology leads to a poorly understood complex dynamic behavior in both models we classify the agents via their interconnection topology and accordingly compute the equilibria of the system then we define a positive invariant set centered at each equilibrium opinion vector we show that if a trajectory enters one such set then it converges to a steady state with consta

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

synchronization in a system of globally coupled oscillators with time delay we study the synchronization phenomena in a system of globally coupled oscillators with time delay in the coupling the self consistency equations for the order parameter are derived which depend explicitly on the amount of delay analysis of these equations reveals that the system in general exhibits discontinuous transitions in addition to the usual continuous transition between the incoherent state and a multitude of coherent states with different synchronization frequencies in particular the phase diagram is obtained on the plane of the coupling strength and the delay time and ubiquity of multistability as well as suppression of the synchronization frequency is manifested numerical simulations are also performed to give consistent results

solving multiobjective multiconstraint knapsack problems using mathematical programming and evolutionary algorithms abstract in this paper we solve instances of the multiobjective multiconstraint or multidimensional knapsack problem momckp from the literature with three objective functions and three constraints we use exact as well as approximate algorithms the exact algorithm is a properly modified version of the multicriteria branch and bound mcbb algorithm which is further customized by suitable heuristics three branching heuristics and a more general purpose composite branching and construction heuristic are devised comparison is made to the published results from another exact algorithm the adaptive e constraint method laumanns m thiele l zitzler e 2006 an efficient adaptive parameter variation scheme for metaheuristics based on the epsilon constraint method european journal of operational research 169 932 942 using the same data sets furthermore the same problems are solved using standard multiobjective evolutionary algorithms moea namely the spea2 and the nsgaii the results from the exact case show that the branching heuristics greatly improve the performance of the mcbb algorithm which becomes faster than the adaptive e constraint regarding the performance of the moea algorithms in the specific problems spea2 outperforms nsgaii in the degree of approximation of the pareto front as measured by the coverage metric especially for the largest instance

stability and bifurcations in neural fields with finite propagation speed and general connectivity a stability analysis is presented for neural field equations in the presence of finite propagation speed along axons and for a general class of connectivity kernels and synaptic proper ties sufficient conditions are given for the stability of equilibrium solutions it is shown that the propagation delays play a significant role in nonstationary bifurcations of equilibria whereas the stationary bifurcations depend only on the connectivity kernel in the case of nonstationary bifurca tions bounds are determined on the frequencies of the resulting oscillatory solutions a perturbative scheme is used to calculate the types of bifurcations leading to spatial patterns oscillations and traveling waves for high propagation speeds a simple method is derived that allows the determi nation of the bifurcation type by visual inspection of the fourier transforms of the kernel and its first moment results are numerically illustrated on a class of neurologically plausible systems with combinations of gaussian excitatory and inhibitory connections

normal boundary intersection a new method for generating the pareto surface in nonlinear multicriteria optimization problems this paper proposes an alternate method for finding several pareto optimal points for a general nonlinear multicriteria optimization problem such points collectively capture the trade off among the various conflicting objectives it is proved that this method is independent of the relative scales of the functions and is successful in producing an evenly distributed set of points in the pareto set given an evenly distributed set of parameters a property which the popular method of minimizing weighted combinations of objective functions lacks further this method can handle more than two objectives while retaining the computational efficiency of continuation type algorithms this is an improvement over continuation techniques for tracing the trade off curve since continuation strategies cannot easily be extended to handle more than two objectives

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

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

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

inertial hegselmann krause systems we derive an energy bound for inertial hegselmann krause hk systems which are a variant of the classic hk model that allows agents to change weights as they please at each step we use the bound to prove the convergence of hk systems with static agents which settles a widely believed conjecture this paper also introduces anchored hk systems and show their equivalence to the symmetric heterogeneous model

opinion evolution analysis for short range and long range deffuant weisbuch models abstract in this paper we propose and then analyze two generalized deffuant weisbuch dw models the generalized models extend the conventional dw model by taking multiple choices in two different ways first we demonstrate the almost sure convergence of the agent opinions for the short range multi choice dw dynamics when only the opinions within confidence regions may be count in then we analyze dynamical behavior about the long range multi choice dw model when some opinions out of the confidence ranges are considered with a weighted combination moreover both theoretical and simulation results show that the dynamical behaviors of the two models are totally different

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

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

phase locked patterns and amplitude death in a ring of delay coupled limit cycle oscillators we study the existence and stability of phase locked patterns and amplitude death states in a closed chain of delay coupled identical limit cycle oscillators that are near a supercritical hopf bifurcation the coupling is limited to nearest neighbors and is linear we analyze a model set of discrete dynamical equations using the method of plane waves the resultant dispersion relation which is valid for any arbitrary number of oscillators displays important differences from similar relations obtained from continuum models we discuss the general characteristics of the equilibrium states including their dependencies on various system parameters we next carry out a detailed linear stability investigation of these states in order to delineate their actual existence regions and to determine their parametric dependence on time delay time delay is found to expand the range of possible phase locked patterns and to contribute favorably toward their stability the amplitude death state is studied in the parameter space of time delay and coupling strength it is shown that death island regions can exist for any number of oscillators n in the presence of finite time delay a particularly interesting result is that the size of an island is independent of n when n is even but is a decreasing function of n when n is odd

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

consensus reaching in multi agent packet switched networks with non linear coupling an important task for multi agent systems mas is to reach a consensus e g to align their velocity vectors recent results propose appropriate consensus protocols to achieve such tasks but most of them do not consider the effect of communication constraints such as the presence of time delays in the exchange of information between the agents in this article we provide conditions for a non linear locally passive mas of arbitrary size to reach a consensus when the agents communicate over a packet switched network that is characterised by a given topology both the cases of constant and switching topologies are considered the nature of the communication channel imposes constraints that are modelled using stochastic delays of arbitrary distribution we first embed this model in another distributed but deterministic delay model and provide conditions for the error introduced by this simplification in our main result we provide conditions for the locally passive mas with distributed delays to reach

phase models with explicit time delays studying weakly connected oscillators leads to phase models it has been proven recently that weakly connected oscillators with delayed interactions do not lead to phase models with time delays even when the delay is of the same order of magnitude as the period of oscillation this has resulted in a fading interest in such models we prove here that if the interaction delay between weakly connected oscillators is much longer than the period of oscillation then the corresponding phase model does have an explicit time delay

transition from anticipatory to lag synchronization via complete synchronization in time delay systems the existence of anticipatory complete and lag synchronization in a single system having two different time delays that is feedback delay tau1 and coupling delay tau2 is identified the transition from anticipatory to complete synchronization and from complete to lag synchronization as a function of coupling delay tau2 with a suitable stability condition is discussed in particular it is shown that the stability condition is independent of the delay times tau1 and tau2 consequently for a fixed set of parameters all the three types of synchronizations can be realized further the emergence of exact anticipatory complete or lag synchronization from the desynchronized state via approximate synchronization when one of the system parameters b2 is varied is characterized by a minimum of the similarity function and the transition from on off intermittency via periodic structure in the laminar phase distribution

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

a stabilization theorem for dynamics of continuous opinions abstract a stabilization theorem for processes of opinion dynamics is presented the theorem is applicable to a wide class of models of continuous opinion dynamics based on averaging like the models of hegselmann krause and weisbuch deffuant the analysis detects self confidence as a driving force of stabilization

generating a representative subset of the nondominated frontier in multiple criteria decision making in this paper we address the problem of generating a discrete representation of the nondominated frontier in multiple objective linear problems we find a surface that approximates the shape of the nondominated frontier utilizing the surface we generate a set of discrete points that is representative of the frontier our experience on randomly generated problems demonstrates that the approach performs well in terms of both the quality of the representation and the computation time

cluster synchronization stability for stochastic complex dynamical networks with probabilistic interval time varying delays the paper investigates the cluster synchronization stability problem for a class of complex dynamical networks with stochastic nonlinearities and probabilistic interval time varying delays the stochastic nonlinearities are considered here to reflect more realistic dynamical behaviors of complex networks the delay in this paper is assumed to be random and its probability distribution is known a priori based on the stochastic analysis techniques and the properties of the kronecker product delay dependent cluster synchronization stability criteria are derived in the form of linear matrix inequalities which can be readily solved by using the lmi toolbox in matlab the solvability of derived conditions depends on not only the size of the delay but also the probability of the delay taking values in some intervals finally a numerical example is given to illustrate the feasibility and effectiveness of the proposed method

synchronization of networks of chaotic units with time delayed couplings a network of chaotic units is investigated where the units are coupled by signals with a transmission delay any arbitrary finite network is considered where the chaotic trajectories of the uncoupled units are a solution of the dynamic equations of the network it is shown that chaotic trajectories cannot be synchronized if the transmission delay is larger than the time scales of the individual units for several models the master stability function is calculated which determines the maximal delay time for which synchronization is possible

frequency synchronization and phase agreement in kuramoto oscillator networks with delays we investigate frequency synchronization and phase agreement in networks of non identical kuramoto oscillators with delayed coupling we provide delay dependent lower bounds for the coupling gain so that a network with all to all coupling and constant heterogeneous delays achieves synchronization the given bounds are determined explicitly by the system parameters furthermore we show that frequency synchronization and phase agreement are possible in general directed networks of non identical oscillators which contain a spanning tree if the delays satisfy a self consistency condition networks with delays differ at this point notably from networks without delays because phase agreement is not possible in undelayed non identical kuramoto oscillator networks in addition to the sufficient conditions for synchronization we investigate the connection between phase agreement and the existence of solutions of a necessary self consistency condition

on approximations and ergodicity classes in random chains we study the limiting behavior of a random dynamic system driven by a stochastic chain our interest is in the chains that are not necessarily ergodic but are decomposable into ergodic classes to investigate the conditions under which the ergodic classes of a model can be identified we introduce and study an l1 approximation and infinite flow graph of the model we show that the l1 approximations of random chains preserve certain limiting behavior using the l1 approximations we show how the connectivity of the infinite flow graph is related to the structure of the ergodic groups of the model our main result of this paper provides conditions under which the ergodicity groups of the model can be identified by considering the connected components in the infinite flow graph we provide two applications of our main result to random networks namely broadcast over time varying networks and networks with random link failure

isochronal synchronization of time delay and delay coupled chaotic systems this paper studies the problem of isochronal synchronization of time delay chaotic systems featuring also coupling delay based on the lyapunov krasovskii stability theory sufficient conditions are derived for the stability of isochronal synchronization between a pair of identical chaotic systems such criteria permit the proper design of stable proportional linear feedback controller more specifically the design of adequate proportional feedback gain matrices the proposed criteria are suited to systems with i intrinsic delay ii coupling delay or iii both numerical simulations of the synchronization of delay coupled systems are presented as examples of the application of the criteria

adaptive decision dynamics bifurcations multistability and chaos abstract in this paper we propose a model describing the dynamical process of decision and opinion formation of two economic homogeneous interacting and boundedly rational agents the decisional process represented in our model is given by an adaptive adjustment mechanism in which two agents take into account the difference between their own opinion and the opinion of the other agent the smaller that difference the larger the weight given to the comparison of the opinions by means of an auxiliary variable describing the distance between the opinions we obtain a one dimensional dynamical system for which we investigate via analytical and numerical tools the stability of the unique steady state its bifurcations as well as the existence of a globally absorbing interval and of chaotic dynamics we also investigate multistability phenomena i e the presence of coexisting attractors finally we relax the assumption of homogeneity between agents and we show that there is a strong correspondence between the dynamic behaviors in the scenarios with and without homogeneity

opinion dynamics with decaying confidence application to community detection in graphs we study a class of discrete time multi agent systems modeling opinion dynamics with decaying confidence we consider a network of agents where each agent has an opinion at each time step the agents exchange their opinion with their neighbors and update it by taking into account only the opinions that differ from their own less than some confidence bound this confidence bound is decaying an agent gives repetitively confidence only to its neighbors that approach sufficiently fast its opinion essentially the agents try to reach an agreement with the constraint that it has to be approached no slower than a prescribed convergence rate under that constraint global consensus may not be achieved and only local agreements may be reached the agents reaching a local agreement form communities inside the network in this paper we analyze this opinion dynamics model we show that communities correspond to asymptotically connected components of the network and give an algebraic characterization of communities in terms of eigenvalues of the matrix defining the collective dynamics finally we apply our opinion dynamics model to address the problem of community detection in graphs we propose a new formulation of the community detection problem based on eigenvalues of normalized laplacian matrix of graphs and show that this problem can be solved using our opinion dynamics model we consider three examples of networks and compare the communities we detect with those obtained by existing algorithms based on modularity optimization we show that our opinion dynamics model not only provides an appealing approach to community detection but that it is also effective

the convergence of bird flocking we bound the time it takes for a group of birds to stabilize in a standard flocking model each bird averages its velocity with its neighbors lying within a fixed radius we resolve the worst case complexity of this natural algorithm by providing asymptotically tight bounds on the time to equilibrium we reduce the problem to two distinct questions in computational geometry and circuit complexity

wave formation by time delays in randomly coupled oscillators we study the dynamics of randomly coupled oscillators when interactions between oscillators are time delayed due to the finite and constant speed of coupling signals numerical simulations show that the time delays proportional to the euclidean distances between interacting oscillators can induce near regular waves in addition to near in phase synchronous oscillations even though oscillators are randomly coupled we discuss the stability conditions for the wave states and the in phase synchronous states

min max time consensus tracking with communication guarantee in this paper a collection of double integrator agents with bounded inputs is considered communication is possible between any two agents only if the inter agent distance is less than a fixed threshold a special node referred to as the leader generates an unknown reference trajectory to which all the other agents are required to converge in the shortest possible time assuming the initial communication graph to be connected a directed spanning tree rooted at the leader is identified using a local algorithm the dynamics of any two agents connected by an edge in the selected tree are modeled as a time optimal pursuit evasion game while maintaining the inter agent communication link using the corresponding feedback saddle point strategies local min max time control laws for each pair of agents are formulated for the selected tree the proposed collection of local min max time control strategies is shown to be the communication preserving global min max time strategy

reaching consensus on rumors abstract an important contribution in sociophysics is the galam s model of rumors spreading this model provides an explanation of rumors spreading in a population and explains some interesting social phenomena such as the diffusion of hoaxes in this paper the model has been reformulated as a markov process highlighting the stochastic nature of the phenomena this formalization allows us to derive conditions for consensus to be reached and for the existence of some interesting phenomena such as the emergence of impasses the proposed formulation allows a deeper and more comprehensive analysis of the diffusion of rumors

normal constraint method with guarantee of even representation of complete pareto frontier multiobjective optimization is rapidly becoming an invaluable tool in engineering design a particular class of solutions to the multiobjective optimization problem is said to belong to the pareto frontier a pareto solution the set of which comprises the pareto frontier is optimal in the sense that any improvement in one design objective can only occur with the worsening of at least one other accordingly the pareto frontier plays an important role in engineering design it characterizes the tradeoffs between conflicting design objectives some optimization methods can be used to automatically generate a set of pareto solutions from which a final design is subjectively chosen by the designer for this approach to be successful the generated pareto set must be truly representative of the complete optimal design space pareto frontier in other words the set must not overrepresent one region of the design space or neglect others some commonly used methods comply with this requirement whereas others do not this paper offers a new phase in the development of the normal constraint method which is a simple approach for generating pareto solutions that are evenly distributed in the design space of an arbitrary number of objectives the even distribution of the generated pareto solutions can facilitate the process of developing an analytical expression for the pareto frontier in n dimension an even distribution of pareto solutions also facilitates the task of choosing the most desirable final design from among the set of pareto solutions the normal constraint method bears some similarities to the normal boundary intersection and constraint methods importantly the developments presented in this paper define its critical distinction namely the ability to generate a set of evenly distributed pareto solutions over the complete pareto frontier examples are provided that show the normal constraint method to perform favorably under the new developments when compared with the normal boundary intersection method as well as with the original normal constraint method

characterization of almost surely continuous 1 stable random fourier series and strongly stationary processes we complete the results of m marcus and g pisier by showing that a strongly stationary 1 stable process x t t g defined on a locally compact group has a version with sample continuous paths if and only if the entropy integral 0 log log n k d x e de is finite where k is a given neighborhood of the unit and d x is the distance induced by the process

characterizations of almost surely continuous p stable random fourier series and strongly stationary processes on etend le probleme de dudley fernique aux processus p stables fortement stationnaires 1 p 2

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

synchronization of chaotic networks with time delayed couplings an analytic study networks of nonlinear units with time delayed couplings can synchronize to a common chaotic trajectory although the delay time may be very large the units can synchronize completely without time shift for networks of coupled bernoulli maps analytic results are derived for the stability of the chaotic synchronization manifold for a single delay time chaos synchronization is related to the spectral gap of the coupling matrix for networks with multiple delay times analytic results are obtained from the theory of polynomials finally the analytic results are compared with networks of iterated tent maps and lang kobayashi equations which imitate the behavior of networks of semiconductor lasers

convergence properties of the heterogeneous deffuant weisbuch model the deffuant weisbuch dw model is a bounded confidence opinion dynamics model that has attracted much recent interest despite its simplicity and appeal the dw model has proved technically hard to analyze and its most basic convergence properties easy to observe numerically are only conjectures this paper solves the convergence problem for the heterogeneous dw model with the weighting factor not less than 1 2 we establish that for any positive confidence bounds and initial values the opinion of each agent will converge to a limit value almost surely and the convergence rate is exponential in mean square moreover we show that the limiting opinions of any two agents either are the same or have a distance larger than the confidence bounds of the two agents finally we provide some sufficient conditions for the heterogeneous dw model to reach consensus

strong effects of network architecture in the entrainment of coupled oscillator systems random networks of coupled phase oscillators representing an approximation for systems of coupled limit cycle oscillators are considered entrainment of such networks by periodic external forcing applied to a subset of their elements is numerically and analytically investigated for a large class of interaction functions we find that the entrainment window with a tongue shape becomes exponentially narrow for networks with higher hierarchical organization however the entrainment is significantly facilitated if the networks are directionally biased i e closer to the feedforward networks furthermore we show that the networks with high entrainment ability can be constructed by evolutionary optimization processes the neural network structure of the master clock of the circadian rhythm in mammals is discussed from the viewpoint of our results

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

the total s energy of a multiagent system we introduce the total s energy of a multiagent system with time dependent links this provides a new analytical perspective on bidirectional agreement dynamics which we use to bound the convergence rates of dynamical systems for synchronization flocking opinion dynamics and social epistemology

opinion fluctuations and disagreement in social networks we study a tractable opinion dynamics model that generates long run disagreements and persistent opinion fluctuations our model involves an inhomogeneous stochastic gossip process of continuous opinion dynamics in a society consisting of two types of agents 1 regular agents who update their beliefs according to information that they receive from their social neighbors and 2 stubborn agents who never update their opinions and might represent leaders political parties or media sources attempting to influence the beliefs in the rest of the society when the society contains stubborn agents with different opinions the belief dynamics never lead to a consensus among the regular agents instead beliefs in the society fail to converge almost surely the belief profile keeps on fluctuating in an ergodic fashion and it converges in law to a nondegenerate random vector the structure of the graph describing the social network and the location of the stubborn agents within it shape the opinion dynamics the expected belief vector is proved to evolve according to an ordinary differential equation coinciding with the kolmogorov backward equation of a continuous time markov chain on the graph with absorbing states corresponding to the stubborn agents and hence to converge to a harmonic vector with every regular agent s value being the weighted average of its neighbors values and boundary conditions corresponding to the stubborn agents beliefs expected cross products of the agents beliefs allow for a similar characterization in terms of coupled markov chains on the graph describing the social network we prove that in large scale societies which are highly fluid meaning that the product of the mixing time of the markov chain on the graph describing the social network and the relative size of the linkages to stubborn agents vanishes as the population size grows large a condition of homogeneous influence emerges whereby the stationary beliefs marginal distributions of most of the regular agents have approximately equal first and second moments

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

a heuristic for estimating nadir criterion values in multiple objective linear programming in this paper we further investigate the problem of finding nadir criterion values minimum criterion values over the nondominated set in multiple objective linear programming although easy to obtain the minimum values present in a payoff table are unreliable and should only be used with caution especially in problems that have more than a small number of extreme points to obtain better estimates of the nadir criterion values without adding great complexity to the task we present an approach based upon the use of reference directions at each iteration of this approach a reference direction is chosen that maximally minimizes the objective under consideration we proceed with reference directions that accomplish this until the objective under consideration reaches a local minimum over the nondominated set then a cutting plane is inserted into the problem and another direction if one can be found that maximally minimizes the objective under consideration is employed although the method is heurist

convergence speed in distributed consensus and averaging we study the convergence speed of distributed iterative algorithms for the consensus and averaging problems with emphasis on the latter we first consider the case of a fixed communication topology we show that a simple adaptation of a consensus algorithm leads to an averaging algorithm we prove lower bounds on the worst case convergence time for various classes of linear time invariant distributed consensus methods and provide an algorithm that essentially matches those lower bounds we then consider the case of a time varying topology and provide a polynomial time averaging algorithm

nonlinear regulation the piecewise linear approach this paper approaches nonlinear control problems through the use of discrete time piecewise linear systems these are systems whose next state and output maps are both described by pl maps i e by maps which are affine on each of the components of a finite polyhedral partition various results on state and output feedback observers and inverses standard for linear systems are proved for pl systems many of these results are then used in the study of more general both discrete and continuous time systems using suitable approximations

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

extreme fluctuations in stochastic network coordination with time delays we study the effects of uniform time delays on the extreme fluctuations in stochastic synchronization and coordination problems with linear couplings in complex networks we obtain the average size of the fluctuations at the nodes from the behavior of the underlying modes of the network we then obtain the scaling behavior of the extreme fluctuations with system size as well as the distribution of the extremes on complex networks and compare them to those on regular one dimensional lattices for large complex networks when the delay is not too close to the critical one fluctuations at the nodes effectively decouple and the limit distributions converge to the fisher tippett gumbel density in contrast fluctuations in low dimensional spatial graphs are strongly correlated and the limit distribution of the extremes is the airy density finally we also explore the effects of nonlinear couplings on the stability and on the extremes of the synchronization landscapes

strategic influence in social networks we consider a model of influence with a set of non strategic agents and two strategic agents the non strategic agents have initial opinions and are linked through a simply connected network they update their opinions as in the degroot model the two strategic agents have fixed opinions 1 and 0 respectively and are characterized by the magnitude of the impact they can exert on non strategic agents each strategic agent forms a link with one non strategic agent in order to alter the average opinion that eventually emerges in the network this procedure defines a zero sum game whose players are the two strategic agents and whose strategy set is the set of non strategic agents we focus on the existence and the characterization of equilibria in pure strategy in this setting simple examples show that the existence of a pure strategy equilibrium does depend on the structure of the network the characterization of equilibrium we obtain emphasizes on the one hand the influenceability of target agents and on the other hand their centrality whose natural measure in our context defines a new concept related to betweenness centrality that we call intermediacy we also show that in the case where the two strategic agents have the same impact symmetric equilibria emerge as natural solutions whereas in the case where the impacts are uneven the strategic players generally have differentiated equilibrium targets the high impacts agent focusing on centrality and the low impact agent on influenceability

product of random stochastic matrices the paper deals with the convergence properties of the products of random row stochastic matrices the limiting behavior of such products is studied from a dynamical system point of view in particular by appropriately defining a dynamic associated with a given sequence of random row stochastic matrices we prove that the dynamics admits a class of time varying lyapunov functions including a quadratic one then we discuss a special class of stochastic matrices a class p which plays a central role in this work we then study cut balanced chains and using some geometric properties of these chains we characterize the stability of a subclass of cut balanced chains as a special consequence of this stability result we obtain an extension of a central result in the non negative matrix theory stating that for any aperiodic and irreducible row stochastic matrix a the limit limk ak exists and it is a rank one stochastic matrix we show that a generalization of this result holds not only for sequences of stochastic matrices but also for independent random sequences of such matrices

stability of synchronized states in networks of phase oscillators the stability of synchronized states frequency locked states in networks of phase oscillators is investigated for several network topologies it is shown that for some topologies there is more than one stable synchronized state according to the sign of coupling strength between oscillators it is also shown that in some cases the synchronized state corresponds to zero order parameter

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

interaction ruling animal collective behavior depends on topological rather than metric distance evidence from a field study numerical models indicate that collective animal behavior may emerge from simple local rules of interaction among the individuals however very little is known about the nature of such interaction so that models and theories mostly rely on aprioristic assumptions by reconstructing the three dimensional positions of individual birds in airborne flocks of a few thousand members we show that the interaction does not depend on the metric distance as most current models and theories assume but rather on the topological distance in fact we discovered that each bird interacts on average with a fixed number of neighbors six to seven rather than with all neighbors within a fixed metric distance we argue that a topological interaction is indispensable to maintain a flock s cohesion against the large density changes caused by external perturbations typically predation we support this hypothesis by numerical simulations showing that a topological interaction grants significantly higher cohesion of the aggregation compared with a standard metric one

on finding multiple pareto optimal solutions using classical and evolutionary generating methods in solving multi objective optimization problems evolutionary algorithms have been adequately applied to demonstrate that multiple and well spread pareto optimal solutions can be found in a single simulation run in this paper we discuss and put together various different classical generating methods which are either quite well known or are in oblivion due to publication in less accessible journals and some of which were even suggested before the inception of evolutionary methodologies these generating methods specialize either in finding multiple pareto optimal solutions in a single simulation run or specialize in maintaining a good diversity by systematically solving a number of scalarizing problems most classical generating methodologies are classified into four groups mainly based on their working principles and one representative method from each group is chosen in the present study for a detailed discussion and for its performance comparison with a state of the art evolutionary method on visual comparisons of the efficient frontiers obtained for a number of two and three objective test problems the results bring out interesting insights about the strengths and weaknesses of these approaches the results should motivate researchers to design hybrid multi objective optimization algorithms which may be better than each of the individual methods

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

synchronization in oscillator networks with delayed coupling a stability criterion we derive a stability criterion for the synchronous state in networks of identical phase oscillators with delayed coupling the criterion applies to any network whether regular or random low dimensional or high dimensional directed or undirected in which each oscillator receives delayed signals from k others where k is uniform for all oscillators

well posedness of the limiting equation of a noisy consensus model in opinion dynamics abstract this paper establishes the global well posedness of the nonlinear fokker planck equation for a noisy version of the hegselmann krause model the equation captures the mean field behavior of a classic multiagent system for opinion dynamics we prove the global existence uniqueness nonnegativity and regularity of the weak solution we also exhibit a global stability condition which delineates a forbidden region for consensus formation this is the first nonlinear stability result derived for the hegselmann krause model

karhunen loeve decomposition approach to analyzing complex network synchronization in this paper the approach of the karhunen lo ve decomposition known also as the proper orthogonal modes poms is taken to analyze phase synchronization of various complex networks with different topologies namely the classic kuramoto model coupled chaotic maps with gaussian delays and a chain of diffusively coupled bistable oscillators in the case of the kuramoto model the poms reveal the tendency and the level of synchronization with the increase of the coupling strength for globally coupled networks and scale free networks while periodic poms are found in nearest neighbor coupled networks furthermore for cluster networks on the kuramoto model the first leading poms based on different time intervals reveal that different sub groups of nodes synchronize gradually to different levels eventually leading to the complete phase synchronization in the case of coupled chaotic maps some properties of phase synchronization change with the coupling strength value in the case of the chain of diffusively coupled bistable oscillators several main poms not only determine the network phase synchronization but also provide good reconstruction of the network responses

emergent behavior in flocks we provide a model for both continuous and discrete time describing the evolution of a flock our model is parameterized by a constant beta capturing the rate of decay which in our model is polynomial of the influence between birds in the flock as they separate in space our main result shows that when beta 1 2 convergence of the flock to a common velocity is guaranteed while for betages1 2 convergence is guaranteed under some condition on the initial positions and velocities of the birds only

synchronization and balancing on the n torus in this paper we study the behavior of a network of n agents each evolving on the circle we propose a novel algorithm that achieves synchronization or balancing in phase models under mild connectedness assumptions on the possibly time varying and unidirectional communication graphs the global convergence analysis on the n torus is a distinctive feature of the present work with respect to previous results that have focused on convergence in the euclidean space

the cross entropy method in multi objective optimisation an assessment solving multi objective problems requires the evaluation of two or more conflicting objective functions which often demands a high amount of computational power this demand increases rapidly when estimating values for objective functions of dynamic stochastic problems since a number of observations are needed for each evaluation set of which there could be many computer simulation applications of real world optimisations often suffer due to this phenomenon evolutionary algorithms are often applied to multi objective problems in this article the cross entropy method is proposed as an alternative since it has been proven to converge quickly in the case of single objective optimisation problems we adapted the basic cross entropy method for multi objective optimisation and applied the proposed algorithm to known test problems this was followed by an application to a dynamic stochastic problem where a computer simulation model provides the objective function set the results show that acceptable results can be obtained while doing relatively few evaluations