In the 1D swarmalator model with uniform coupling disorder, a coupling-split cluster emerges with order parameter fixed by positive-coupling excess, alongside altered stability of async, sync, and phase-wave states including a Bogdanov-Takens point.
Topological transitions in swarmalators systems
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abstract
After its development, the swarmalators model attracted a great deal of attention since it was found to be very suitable to reproduce several behaviors in collective dynamics. However, few works explain the transitions that are observed while varying system parameters. In this letter, we demonstrate that the changes observed in swarmalator dynamics are governed by changes in the system's topology. To provide a deeper understanding of these changes, we present a topological framework for the swarmalator system and determine the topological charge $Q$ and the helicity $\gamma$ of the corresponding topology. Investigations on synchronization and transition to synchronization are studied using this topological charge and the variance of the helicity.
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2026 1verdicts
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Coupling-split clusters in a swarmalator model with uniform coupling disorder
In the 1D swarmalator model with uniform coupling disorder, a coupling-split cluster emerges with order parameter fixed by positive-coupling excess, alongside altered stability of async, sync, and phase-wave states including a Bogdanov-Takens point.