Swarmalators with frequency-weighted interactions
Phys. Rev. E 113, 034216 – Published 17 March, 2026
DOI: https://doi.org/10.1103/dhz7-p4yg
Abstract
We investigate the role of frequency-weighted interactions in a solvable model of one-dimensional swarmalators confined to a ring, where both spatial and phase couplings are scaled by the heterogeneous natural frequencies of individual agents. Our analysis identifies three distinct collective states: the asynchronous state, the phase-wave state, and the bistrip mixed state characterized by antipodal clusters that are internally split into frequency-dependent substrips. We further establish that the onset of abrupt transitions are driven by heterogeneous coupling. Using a self-consistency analysis, we precisely determine the conditions for dynamical transitions among the identified states, thereby extending the theoretical understanding of swarmalator dynamics under heterogeneous interaction rules, which are in good agreement with the numerical simulation results.
