The Sakaguchi-Kuramoto model in presence of asymmetric interactions that break phase-shift symmetry

TL;DR

This paper extends the Sakaguchi-Kuramoto model by introducing asymmetric interactions that break phase-shift symmetry, revealing complex bifurcation structures and multiple synchronized states.

Contribution

It introduces a novel generalization of the Sakaguchi-Kuramoto model with asymmetric interactions, uncovering new bifurcation phenomena and coexistence states.

Findings

Rich bifurcation diagram with oscillatory and non-oscillatory states

Existence of two-state and three-state coexistence regions

Unveiling of previously unexplored synchronization phenomena

Abstract

The celebrated Kuramoto model provides an analytically tractable framework to study spontaneous collective synchronization and comprises globally coupled limit-cycle oscillators interacting symmetrically with one another. The Sakaguchi-Kuramoto model is a generalization of the basic model that considers the presence of a phase-lag parameter in the interaction, thereby making it asymmetric between oscillator pairs. Here, we consider a further generalization, by adding an interaction that breaks the phase-shift symmetry of the model. The highlight of our study is the unveiling of a very rich bifurcation diagram comprising of both oscillatory and non-oscillatory synchronized states as well as an incoherent state: There are regions of two-state as well as an interesting and hitherto unexplored three-state coexistence arising from asymmetric interactions in our model.