Synchronization and spatial patterns in forced swarmalators

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.

8 pages, 6 figures

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• Collective steady-state patterns of swarmalators with finite-cutoff interaction distance
• Dynamics of swarmalators: A pedagogical review
• Attractive and repulsive interactions in the one-dimensional swarmalator model
• Swarmalators on a ring with uncorrelated pinning
• Generalized frustration in the multidimensional Kuramoto model
• Order, chaos, and dimensionality transition in a system of swarmalators
• Bifurcations in the Kuramoto model with external forcing and higher-order interactions
• Coupling disorder in a population of swarmalators