Discontinuous transition to synchrony in the Kuramoto-Sakaguchi model with a uniform distribution of frequencies

TL;DR

This paper extends the theory of discontinuous synchronization transitions in the Kuramoto model to include phase shifts, analyzing how order parameters depend on coupling strength and phase shift, revealing two distinct transitions.

Contribution

It introduces a theoretical extension of the Kuramoto-Sakaguchi model, accounting for phase shifts and describing the nature of synchronization transitions.

Findings

The transition to synchrony is discontinuous in the model.

Two transitions occur: from disorder to partial synchrony, then to complete synchrony.

The first transition's jump size varies with phase shift, becoming exponentially small near π/2.

Abstract

The transition to synchrony in the Kuramoto model of globally coupled phase oscillators with a uniform distribution of natural frequencies is discontinuous. We extend the theory of this transition to the Kuramoto-Sakaguchi model, taking into account a phase shift in coupling. In the thermodynamic limit, we derive dependencies of the order parameters on the coupling strength and the phase shift, and describe two transitions from disorder to partial synchrony and from partial synchrony to complete synchrony. In all cases, the first transition is discontinuous, although for phase shifts close to $\pi/2$, the jump is exponentially small.