Time delay in the 1d swarmalator model
Adaptation and Self-Organizing Systems
2026-02-10 v1 Statistical Mechanics
Abstract
We study the 1d swarmalator model augmented with time delayed coupling. Along with the familiar sync, async, and phase wave states, we find a family of unsteady states where the order parameters are time periodic, sometimes with clean oscillations, sometimes with irregular vacillations. The unsteady states are born in two ways: via a Hopf bifurcation from the phase wave, and a zero eigenvalue bifurcation from the async state. We find both of these boundary curves analytically. A surprising result is that stabilities of the async and sync states are independent of the delay {\tau}; they depend only on the coupling strength.
Cite
@article{arxiv.2602.08156,
title = {Time delay in the 1d swarmalator model},
author = {K. P. O'Keeffe and Jason Hindes},
journal= {arXiv preprint arXiv:2602.08156},
year = {2026}
}