Swarmalators with Higher Harmonic Coupling: Clustering and Vacillating

Abstract

SIAM Journal on Applied Dynamical Systems, Volume 23, Issue 2, Page 1133-1158, June 2024.
Abstract.We study the dynamics of a swarmalator model with higher harmonic phase coupling. We analyze stability, bifurcation, and structural properties of several novel attracting states, including the formation of spatial clusters with distinct phases, and single spatial clusters with a small number of distinct phases. We use mean-field (centroid) dynamics to analytically determine intercluster distance. We also find states with two large clusters along with a small number of swarmalators that are trapped between the two clusters and vacillate (waver) between them. In the case of a single vacillator we use a mean-field reduction to reduce the dynamics to two dimensions, which enables a detailed bifurcation analysis. We show excellent agreement between our reduced two-dimensional model and the dynamics and bifurcations of the full swarmalator model.