Role of Coupling Asymmetry in the Fully Disordered Kuramoto Model

TL;DR

This paper explores how coupling asymmetry affects the dynamics and phase transition behavior in the fully disordered Kuramoto model, revealing robustness of the volcano transition to small asymmetries and its disappearance with larger antisymmetry.

Contribution

It introduces a mean-field framework for analyzing asymmetric couplings in the Kuramoto model and demonstrates the impact of asymmetry on system correlations and phase transitions.

Findings

Volcano transition remains robust with small asymmetry.

Large antisymmetry in couplings destroys the volcano transition.

Asymmetry influences correlation and response functions.

Abstract

We investigate the dynamics of phase oscillators in the fully disordered Kuramoto model with couplings of defined asymmetry. The mean-field dynamics is reduced to a self-consistent stochastic single-oscillator problem which we analyze perturbatively and by numerical simulations. We elucidate the influence of the asymmetry on the correlation and response function of the system as well as on the distribution of the order parameter. The so-called volcano transition is shown to be robust with respect to a small degree of coupling asymmetry but to disappear when the antisymmetry in the couplings outweighs the symmetry.