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

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.

Accepted for publication in Chaos: An Interdisciplinary Journal of Nonlinear Science

References in corpus (4)

• Low Dimensional Behavior of Large Systems of Globally Coupled Oscillators
• Partially integrable dynamics of hierarchical populations of coupled oscillators
• Synchronization scenarios in the Winfree model of coupled oscillators
• The Kuramoto model in presence of additional interactions that break rotational symmetry

Cited by in corpus (2)

• Synchronization in the Kuramoto model in presence of stochastic resetting
• Nonreciprocity induced spatiotemporal chaos: Reactive vs dissipative routes