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

K. P. O'Keeffe

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arXiv · 2606.10265

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

K. P. O'Keeffe

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Abstract

We study the one-dimensional swarmalator model in which the phase coupling $K_i'$ 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 ($K_i'>0$) from negatively coupled ($K_i'<0$) swarmalators, with smaller order parameter $s=\mu/\gamma$ 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.

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K. P. O'Keeffe. 2026-06-09. Coupling-split clusters in a swarmalator model with uniform coupling disorder. https://arxiv.org/abs/2606.10265

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