• Accepted Paper

Coupling-split clusters in a swarmalator model with uniform coupling disorder

K. P. O’Keeffe

Phys. Rev. E - Accepted 3 November, 2026

DOI: https://doi.org/10.1103/hy6f-3l9c

Abstract

We study the one-dimensional swarmalator model in which the phase coupling Ki is drawn from a uniform distribution. Our main result is a static coupling-split cluster, in which the population partitions across the threshold K = 0 that separates positively coupled (Ki > 0) from negatively coupled (Ki < 0) swarmalators, with smaller order parameter s = µ/γ set by the positive-coupling excess. The familiar async, phase-wave, and sync states persist, but each stability boundary feels a different part of the distribution: async the mean same-coordinate response, sync the most negatively coupled particle, and the phase wave the full density through a logarithmic characteristic equation. At a cusp where its Hopf and real-eigenvalue branches meet, the phase-wave dispersion has a double zero – the spectral signature of a Bogdanov–Takens point – and simulations nearby show a small-amplitude breathing limit cycle. For supports containing strongly negatively coupled particles the order parameters instead oscillate persistently.

Export citation

Export citation

Choose format for download:

Download Citation

If the author has provided any supplemental materials with this article they will be available upon publication of the version of record.

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation