A strategy to control synchronized dynamics in swarmalator systems

TL;DR

This paper introduces a novel Hamiltonian control strategy to suppress synchronization in one-dimensional swarmalator systems, addressing a gap in control methods for spatially moving oscillators.

Contribution

It develops the first control approach specifically designed for swarmalators, combining Hamiltonian control theory with numerical validation.

Findings

Control effectively suppresses synchronization in swarmalator systems.

The number of controlled swarmalators influences control effectiveness.

Simplified control versions maintain suppression capabilities.

Abstract

Synchronization forms the basis of many coordination phenomena in natural systems, enabling them to function cohesively and support their fundamental operations. However, there are scenarios where synchronization disrupts a system's proper functioning, necessitating mechanisms to control or suppress it. While several methods exist for controlling synchronization in non-spatially embedded oscillators, to the best of our knowledge no such strategies have been developed for swarmalators (oscillators that simultaneously move in space and synchronize in time). In this work, we address this gap by introducing a novel control strategy based on Hamiltonian control theory to suppress synchronization in a system of swarmalators confined to a one-dimensional space. The numerical investigations we performed, demonstrate that the proposed control strategy effectively suppresses synchronized dynamics within the swarmalator population. We studied the impact of the number of controlled swarmalators as well as the strength of the control term, in its original form and in a simplified one.