Strategy to control synchronized dynamics in swarmalator systems

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 nonspatially 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 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 and the strength of the control term in its original form and a simplified one.