2024/10/23 by Kevin O’Keeffe, O'Keeffe, Kevin P.
Computer Science · #Nonlinear Dynamics and Pattern Formation #Distributed Control Multi-Agent Systems #Neural Networks Stability and Synchronization
paper · pdf · doi:10.48550/arxiv.2410.18011
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.