Synchronization and spatial patterns in forced swarmalators

TL;DR

This paper investigates how external periodic stimuli influence the synchronization and spatial arrangements of swarmalators, revealing phase transitions and pattern formations such as circular distributions and two-cluster states.

Contribution

It demonstrates the effects of external forcing on swarmalators, including phase locking, correlation decay, and novel spatial patterns, extending understanding beyond fixed-phase oscillators.

Findings

External force induces phase synchronization with the stimulus.

Phase-position correlation decreases with force intensity, leading to a symmetric circular pattern.

Intermediate force causes a stable two-cluster pattern rotating around the stimulus.

Abstract

Swarlamators are particles capable of synchronize and swarm. Here we study the effects produced by an external periodic stimulus over a system of swarmalators that move in two dimensions. When the particles are fixed and interact with equal strength (Kuramoto oscillators) their phases tend to synchronize and lock to the external stimulus if its intensity is sufficiently large. Here we show that in a system of swarmalators the force also shifts the phases and angular velocities leading to synchronization with the external frequency. However, the correlation between phase and spatial location decreases with the intensity of the force, going to zero in what appears to be a second order phase transition. In the regime of zero correlation the particles form a static symmetric circular distribution, following a simple model of aggregation. Interestingly, for intermediate values of the force intensity, a different pattern emerges, with the particles splitting in two clusters centered at opposite sides of the stimulus' location, breaking the radial symmetry. The two-cluster pattern is stable and active, with the clusters slowly rotating around the source while exchanging particles.