Synchronization transitions and sensitivity to asymmetry in the bimodal Kuramoto systems with Cauchy noise

TL;DR

This paper studies how synchronization transitions in large bimodal Kuramoto oscillator systems with Cauchy noise are highly sensitive to asymmetry, revealing universal symmetry-breaking scenarios and new bistability phenomena.

Contribution

It provides an analytical framework using the Ott-Antonsen ansatz to explore the effects of asymmetry on synchronization in bimodal Kuramoto systems with Cauchy noise, uncovering universal behaviors and bistability.

Findings

Small asymmetry stabilizes partially synchronized states.

Universal symmetry-breaking scenario independent of asymmetry type.

Analytical critical values for asymmetry parameters eliminating bistability.

Abstract

We analyze the synchronization dynamics of the thermodynamically large systems of globally coupled phase oscillators under Cauchy noise forcings with bimodal distribution of frequencies and asymmetry between two distribution components. The systems with the Cauchy noise admit the application of the Ott-Antonsen ansatz, which has allowed us to study analytically synchronization transitions both in the symmetric and asymmetric cases. The dynamics and the transitions between various synchronous and asynchronous regimes are shown to be very sensitive to the asymmetry degree whereas the scenario of the symmetry breaking is universal and does not depend on the particular way to introduce asymmetry, be it the unequal populations of modes in bimodal distribution, the phase delay of the Kuramoto-Sakaguchi model, the different values of the coupling constants, or the unequal noise levels in two modes. In particular, we found that even small asymmetry may stabilize the stationary partially synchronized state, and this may happen even for arbitrarily large frequency difference between two distribution modes (oscillator subgroups). This effect also results in the new type of bistability between two stationary partially synchronized states: one with large level of global synchronization and synchronization parity between two subgroups and another with lower synchronization where the one subgroup is dominant, having higher internal (subgroup) synchronization level and enforcing its oscillation frequency on the second subgroup. For the four asymmetry types, the critical values of asymmetry parameters were found analytically above which the bistability between incoherent and partially synchronized states is no longer possible.