- Accepted Paper
Coupling-split clusters in a swarmalator model with uniform coupling disorder
Phys. Rev. E - Accepted 3 November, 2026
DOI: https://doi.org/10.1103/hy6f-3l9c
Phys. Rev. E - Accepted 3 November, 2026
DOI: https://doi.org/10.1103/hy6f-3l9c
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.
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