Synchronization to extreme events in moving agents (original) (raw)

Distance Dependent Competitive Interactions in a Frustrated Network of Mobile Agents

IEEE Transactions on Network Science and Engineering, 2020

Diverse collective dynamics emerge in dynamical systems interacting on top of complex network architectures. Along this line of research, temporal network has come out to be one of the most promising network platforms to investigate. Especially, such network with spatially moving agents has been established to be capable of modelling a number of practical instances. In this paper, we examine the dynamical outcomes of moving agents interacting based upon their physical proximity. For this, we particularly emphasize on the impact of competing interactions among the agents depending on their physical distance. We specifically assume attractive coupling between agents which are staying apart from each other, whereas we adopt repulsive interaction for agents that are sufficiently close in space. With this setup , we consider two types of coupling configurations, symmetry-breaking and symmetry-preserving couplings. We encounter variants of collective dynamics ranging from synchronization, inhomogeneous small oscillation to cluster state and extreme events while changing the attractive and repulsive coupling strengths. We have been able to map all these dynamical behaviors in the coupling parameter space. Complete synchronization being the most desired state in absence of repulsive coupling, we present an analytical study for this scenario that agrees well with the numerical results.

Random talk: Random walk and synchronizability in a moving neighborhood network

Physica D: Nonlinear Phenomena, 2006

We examine the synchronization problem for a group of dynamic agents that communicate via a moving neighborhood network. Each agent is modeled as a random walker in a finite lattice and is equipped with an oscillator. The communication network topology changes randomly and is dictated by the agents' locations in the lattice. Information sharing (talking) is possible only for geographically neighboring agents. This complex system is a time-varying jump nonlinear system. We introduce the concept of 'long-time expected communication network', defined as the ergodic limit of a stochastic time-varying network. We show that if the long-time expected network supports synchronization, then so does the stochastic network when the agents diffuse sufficiently quickly in the lattice. (D.J. Stilwell), bolltem@clarkson.edu (E.M. Bollt), jskufca@clarkson.edu (J.D. Skufca).

Explosive or Continuous: Incoherent state determines the route to synchronization

2014

Collective behaviors of coupled oscillators have attracted much attention. In this Letter, we propose an ensemble order parameter(EOP) equation that enables us to grasp the essential low-dimensional dynamical mechanism of the explosive synchronization in heterogeneous networks. Dif- ferent solutions of the EOP equation build correspondences with diverse collective states, and different bifurcations reveal various transitions among these collective states. The structural relationship between the incoherent state and synchronous state leads to different routes of transitions to synchronization, either continuous or discontinuous. The explosive synchronization is determined by the bistable state where the measure of each state and the critical points are obtained analytically by using the EOP equation. Our method and results hold for heterogeneous networks with star graph motifs such as scale-free networks, and hence, provide an effective approach in understanding the routes to synchro...

Explosive synchronization in a general complex network

Physical Review E, 2013

Explosive synchronization (ES) has recently attracted much attention, where its two necessary conditions are found to be a scale-free network topology and a positive correlation between the natural frequencies of the oscillators and their degrees. Here we present a framework for ES to be observed in a general complex network, where a positive correlation between coupling strengths of the oscillators and the absolute of their natural frequencies is assumed and the previous studies are included as specific cases. In the framework, the previous two necessary conditions are replaced by another one, thus fundamentally deepening the understanding of the microscopic mechanism toward synchronization. A rigorous analytical treatment by a mean field is provided to explain the mechanism of ES in this alternate framework.

Synchronization of moving oscillators in three dimensional space

Chaos (Woodbury, N.Y.), 2017

We investigate the macroscopic behavior of a dynamical network consisting of a time-evolving wiring of interactions among a group of random walkers. We assume that each walker (agent) has an oscillator and show that depending upon the nature of interaction, synchronization arises where each of the individual oscillators are allowed to move in such a random walk manner in a finite region of three dimensional space. Here, the vision range of each oscillator decides the number of oscillators with which it interacts. The live interaction between the oscillators is of intermediate type (i.e., not local as well as not global) and may or may not be bidirectional. We analytically derive the density dependent threshold of coupling strength for synchronization using linear stability analysis and numerically verify the obtained analytical results. Additionally, we explore the concept of basin stability, a nonlinear measure based on volumes of basin of attractions, to investigate how stable the...

Dynamics and Steady States in Excitable Mobile Agent Systems

Physical Review Letters, 2008

We study the spreading of excitations in 2D systems of mobile agents where the excitation is transmitted when a quiescent agent keeps contact with an excited one during a non-vanishing time. We show that the steady states strongly depend on the spatial agent dynamics. Moreover, the coupling between exposition time (ω) and agent-agent contact rate (CR) becomes crucial to understand the excitation dynamics, which exhibits three regimes with CR: no excitation for low CR, an excited regime in which the number of quiescent agents (S) is inversely proportional to CR, and for high CR, a novel third regime, model dependent, where S scales with an exponent ξ − 1, with ξ being the scaling exponent of ω with CR.

Explosive Synchronization Transitions in Scale-free Networks

Arxiv preprint arXiv: …, 2011

The emergence of explosive collective phenomena has recently attracted much attention due to the discovery of an explosive percolation transition in complex networks. In this Letter, we demonstrate how an explosive transition shows up in the synchronization of complex heterogeneous networks by incorporating a microscopic correlation between the structural and the dynamical properties of the system. The characteristics of this explosive transition are analytically studied in a star graph reproducing the results obtained in synthetic scale-free networks. Our findings represent the first abrupt synchronization transition in complex networks thus providing a deeper understanding of the microscopic roots of explosive critical phenomena. 89.75.Hc, 89.75.Kd Synchronization is one of the central phenomena representing the emergence of collective behavior in natural and synthetic complex systems [1-3]. Synchronization processes describe the coherent dynamics of a large ensemble of interconnected autonomous dynamical units, such as neurons, fireflies or cardiac pacemakers. The seminal works of Watts and Strogatz pointed out the importance of the structure of interactions between units in the emergence of synchronization, which gave rise to the modern framework of complex networks .

Emergence of synchronization in complex networks of interacting dynamical systems

Physica D: Nonlinear Phenomena, 2006

We study the emergence of coherence in large complex networks of interacting heterogeneous dynamical systems. We show that for a large class of dynamical systems and network topologies there is a critical coupling strength at which the systems undergo a transition from incoherent to coherent behavior. We find that the critical coupling strength at which this transition takes place is k c = (Z λ) −1 , where Z depends only on the uncoupled dynamics of the individual systems on each node, while λ is the largest eigenvalue of the network adjacency matrix. Thus we achieve a separation of the problem into two parts, one depending solely on the node dynamics, and one depending solely on network topology.