Synchronization in dynamical networks of locally coupled self-propelled oscillators

TL;DR

This paper investigates how mobility and interactions influence synchronization in networks of self-propelled oscillators, revealing optimal speeds and dynamic regimes that enhance understanding of emergent cooperative behavior in mobile systems.

Contribution

It introduces a simple model of self-propelled oscillators with excluded volume interactions, analyzing synchronization dynamics and identifying regimes with theoretical insights.

Findings

Self-propulsion accelerates synchronization in non-interacting particles.

An optimal self-propulsion speed maximizes synchronization.

Synchronization proceeds via coarsening similar to 2D XY model dynamics.

Abstract

Systems of mobile physical entities exchanging information with their neighborhood can be found in many different situations. The understanding of their emergent cooperative behaviour has become an important issue across disciplines, requiring a general conceptual framework in order to harvest the potential of these systems. We study the synchronization of coupled oscillators in time-evolving networks defined by the positions of self-propelled agents interacting in real space. In order to understand the impact of mobility in the synchronization process on general grounds, we introduce a simple model of self-propelled hard disks performing persistent random walks in 2$d$ space and carrying an internal Kuramoto phase oscillator. For non-interacting particles, self-propulsion accelerates synchronization. The competition between agent mobility and excluded volume interactions gives rise to a richer scenario, leading to an optimal self-propulsion speed. We identify two extreme dynamic regimes where synchronization can be understood from theoretical considerations. A systematic analysis of our model quantifies the departure from the latter ideal situations and characterizes the different mechanisms leading the evolution of the system. We show that the synchronization of locally coupled mobile oscillators generically proceeds through coarsening verifying dynamic scaling and sharing strong similarities with the phase ordering dynamics of the 2$d$ XY model following a quench. Our results shed light into the generic mechanisms leading the synchronization of mobile agents, providing a efficient way to understand more complex or specific situations involving time-dependent networks where synchronization, mobility and excluded volume are at play.