Unsteady phase waves in the 1D swarmalator model with inertia

TL;DR

This paper investigates a one-dimensional swarmalator model with inertia, revealing a new unsteady 'thrashing' phase wave state characterized by multiharmonic oscillations and bifurcations from static states.

Contribution

It introduces the effect of inertia into the 1D swarmalator model, uncovering a novel unsteady phase wave state and analyzing its bifurcation from static configurations.

Findings

Inertia induces a new unsteady 'thrashing' phase wave with multiharmonic oscillations.

The 'thrashing' phase bifurcates from static states via a subcritical Hopf bifurcation.

Small populations exhibit attractor switching between chiral states, larger systems settle on a single state.

Abstract

We study a one-dimensional swarmalator model with inertia. Previous studies have focused almost exclusively on the overdamped limit. We find inertia introduces a new 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.