Mobile oscillators in a mobile multi-cluster network

TL;DR

This paper investigates how the spatial movement of clusters of mobile oscillators influences their synchronization, demonstrating that proximity enhances inter-cluster synchronization and analyzing the stability of intra-cluster synchronization.

Contribution

It introduces a model of multi-cluster mobile oscillators with both external and internal dynamics, analyzing the effects of mobility and spatial proximity on synchronization stability.

Findings

Synchronization within clusters is stable and analytically demonstrated.

Inter-cluster synchronization depends on spatial closeness.

Both analytical and numerical methods confirm the stability results.

Abstract

Different collective behaviors emerging from the unknown have been examined in networks of mobile agents in recent years. Mobile systems, far from being limited to modeling and studying various natural and artificial systems in motion and interaction, offer versatile solutions across various domains, facilitating tasks ranging from navigation and communication to data collection and environmental monitoring. We examine the relative mobility between clusters, each composed of different elements in a multi-clusters network-a system composed of clusters interconnected to form a larger network of mobile oscillators. Each mobile oscillator exhibits both external (i.e., position in a 2D space) and internal dynamics (i.e., phase oscillations). Studying the mutual influence between external and internal dynamics, often leads the system towards a state of synchronization within and between clusters. We show that synchronization between clusters is affected by their spatial closeness. The stability of complete synchronization observed within the clusters is demonstrated through analytical and numerical methods.