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arXiv · 2410.18011

Global synchronization theorem for coupled swarmalators

Kevin P. O'Keeffe
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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.

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Kevin P. O'Keeffe. 2024-10-23. Global synchronization theorem for coupled swarmalators. https://arxiv.org/abs/2410.18011

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