Unsteady phase waves in the one-dimensional swarmalator model with inertia
Phys. Rev. E 113, 064210 – Published 22 June, 2026
DOI: https://doi.org/10.1103/8j2d-539b
Abstract
We study a one-dimensional swarmalator model with inertia. Previous studies have focused almost exclusively on the overdamped limit. We find inertia introduces an unsteady collective state in which the rainbow order parameters undergo multiharmonic oscillations. This “thrashing” phase wave bifurcates from the model's static phase wave state through a subcritical Hopf bifurcation that coincides with a saddle node of limit cycles. The wave itself exists in clockwise and counterclockwise symmetric pairs. For small populations we observe attractor switching between these chiral states, while for larger systems the dynamics settle onto a single branch.
