Desynchronization transitions in nonlinearly coupled phase oscillators

TL;DR

This paper investigates how nonlinear coupling in phase oscillators affects synchronization transitions, revealing mechanisms like cluster states and heteroclinic cycles that influence the shift from synchrony to partial or complex states.

Contribution

It introduces a nonlinear extension of the Kuramoto model with phase-dependent coupling, analyzing bifurcations and transition mechanisms in finite and large oscillator ensembles.

Findings

Small ensembles transition via stable cluster states and heteroclinic cycles.

Larger ensembles exhibit direct transitions to periodic or quasiperiodic regimes.

Bifurcation analysis elucidates the role of nonlinear coupling in synchronization dynamics.

Abstract

We consider the nonlinear extension of the Kuramoto model of globally coupled phase oscillators where the phase shift in the coupling function depends on the order parameter. A bifurcation analysis of the transition from fully synchronous state to partial synchrony is performed. We demonstrate that for small ensembles it is typically mediated by stable cluster states, that disappear with creation of heteroclinic cycles, while for a larger number of oscillators a direct transition from full synchrony to a periodic or quasiperiodic regime occurs.