Coupling disorder in a population of swarmalators

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 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 induce 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 average.

Automated summary

In a system of random coupled oscillators, adjusting the ratio of positive to negative couplings can achieve a phase transition from incoherent to fully synchronized states, with the critical threshold predicted through linear stability analysis. Random couplings induce long-term state patterns, causing oscillators to move based on the location of the quenched couplings. Additionally, systems with mixed randomness for quenched couplings exhibit a combination of deformed patterns understandable through each annealed average.