Circular current induced by angular dynamics in swarmalator populations

Abstract

We propose a modified swarmalator model that generates collective rotational currents in phase synchronization. Our approach builds on the original swarmalator model [4], introducing a key modification: the phase-dependent terms in the spatial dynamics are replaced with a simpler driving term that depends on both the phase and a specified origin. We investigate the dynamics of this model through extensive numerical simulations. When the origin is fixed, spiral motions of synchronized and clustered swarmalators emerge from a finite fraction of random initial conditions, resulting in collective currents. To prevent the unrealistic divergence of these spirals, we introduce a dynamic origin, defined as the center of the swarmalators' positions. With this dynamic origin, the system evolves into rotating collective currents, where synchronized swarmalators form stable circular patterns. In both the fixed and dynamic origin cases, we also observe no-current states, in which synchronized swarmalators aggregate near the origin. Finally, we find that the formation of collective currents can be facilitated by tuning the phase variables either at initialization or during the system's evolution.