Synchronization of moving oscillators in three dimensional space

TL;DR

This paper studies how synchronization emerges among moving oscillators in 3D space with dynamic, intermediate, and possibly unidirectional interactions, deriving conditions for stability and exploring robustness under perturbations.

Contribution

It introduces a novel model of moving oscillators with vision-based interactions in 3D space, deriving analytical thresholds for synchronization and analyzing basin stability.

Findings

Synchronization depends on coupling strength, movement speed, and vision range.

Analytical density-dependent threshold for synchronization is derived.

Basin stability analysis shows robustness of synchronized states under large perturbations.

Abstract

We investigate 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 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.