Global synchronization theorem for coupled swarmalators

TL;DR

This paper proves a global synchronization theorem for mobile oscillators called swarmalators confined to a 1D ring, extending synchronization theory to spatially mobile systems on temporal networks.

Contribution

It introduces a theoretical framework for analyzing synchronization in mobile oscillators, bridging the gap between static network models and real-world moving systems.

Findings

Proves a global stability condition for swarmalator synchronization.

Extends synchronization theory to systems with spatial mobility.

Models movement as a factor in network connectivity on a 1D ring.

Abstract

The global stability of oscillator networks has attracted much recent attention. Ordinarily, the oscillators in such studies are motionless; their spatial degrees of freedom are either ignored (e.g. mean field models) or inactive (e.g geometrically embedded networks like lattices). Yet many real-world oscillators are mobile, moving around in space as they synchronize in time. Here we prove a global synchronization theorem for such swarmalators for a simple model where the units' movements are confined to a 1d ring. This can be thought of as a generalization from oscillators connected on random networks to oscillators connected on temporal networks, where the edges are determined by the oscillators' movements.