Synchronization of moving oscillators in three dimensional space

Abstract

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 synchronous state is under large perturbations. The synchronization phenomenon is analyzed taking limit cycle and chaotic oscillators for wide ranges of parameters like interaction strength k between the walkers, speed of movement v, and vision range r.

Synchronization to extreme events in moving agents

“…In this paper, we consider a planar space in which some identical moving chaotic oscillators interact with each other only when they visit the same restricted regions pre-defined in the planar zone. This interactional platform is thus different from most of the existing studies [19,[34][35][36][37]41] in the field on synchronization of moving agents till now, in which each moving agent is associated with an interaction zone that moves with the agent.…”

“…robots [19], ordered motion in a group of animals [20] and even in the process of chemotaxis [21], this framework has a significant resemblance. Emergence of complete synchronization from different aspects in temporal networks [22][23][24][25][26][27][28][29][30][31][32], particularly among interacting moving oscillators has been investigated previously [19,[33][34][35][36][37][38][39][40][41] and most of these articles considered the framework in which each and every agent always carries a vision shape based on which they create neighbors and interact. In this paper, we consider a planar space in which some identical moving chaotic oscillators interact with each other only when they visit the same restricted regions pre-defined in the planar zone.…”

A simple game and its dynamical richness for modeling synchronization in firefly-like oscillators

“…Synchronization is one of the most common phenomena occurring in oscillating systems in nature and in man-made systems; it inheres to the adjustment of self-sustained oscillators rhythms [1]. Since the beginning of this century, there has been an explosion of studies about synchronization in systems of very different nature such as physical [2][3][4][5][6][7][8][9][10][11][12][13], chemical [14][15][16][17], neuronal [18][19][20][21][22][23][24][25][26], biological [27][28][29][30][31][32][33], and even economic [34]. A paradigmatic example of synchronization is that attained by males of several fireflies species, a phenomenon widely described from qualitative observations [35][36][37], through experiments [38][39][40][41][42][43] or with electronic proxies emulating fireflies [44][45]…”

Taming chimeras in networks through multiplexing delays

“…Due to the finite speed of information transmission, delay naturally arises between the transmission ends (nodes) connected through channels (links) [30]. For instance, in a neural network represented by a multiplex framework where intralayer and interlayer links denote electrical and chemical synapses, respectively, the longer reaction time of the chemical synapses might induce a delay in the interlayer links [31]. In a similar fashion, in a multi-modal transport network where different modes of transportation are denoted by different layers [32], a delay may arise because of passengers switching the mode of transportation.…”