Coupling disorder in a population of swarmalators

TL;DR

This paper investigates how random positive and negative couplings affect the collective behavior of swarmalators, revealing a phase transition to synchronization and pattern formation influenced by coupling randomness.

Contribution

It introduces a model of swarmalators with mixed quenched couplings, analyzing the phase transition and pattern formation through numerical and analytical methods.

Findings

System exhibits phase transition from incoherence to synchronization.

Random couplings induce long-term pattern formations.

Patterns can be understood via annealed averaging of couplings.

Abstract

We consider a population of two-dimensional oscillators with random couplings, and explore the collective states. The coupling strength between oscillators is randomly quenched with two values one of which is positive while the other is negative, and the oscillators can spatially {\it{move}} depending on the state variables for phase and position. We find that the system shows the phase transition from the incoherent state to the fully synchronized one at a proper ratio of the number of positive couplings to the total. The threshold is numerically measured, and analytically predicted by the linear stability analysis of the fully synchronized state. It is found that the random couplings induces the long-term state patterns appearing for constant strength. The oscillators move to the places where the randomly quenched couplings work as if annealed. We further observe that the system with mixed randomnesses for quenched couplings shows the combination of the deformed patterns understandable with each annealed averages.