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

M. Manoranjani; Shamik Gupta; V. K. Chandrasekar

doi:10.1063/5.0055664

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arXiv · 2108.04447

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

M. Manoranjani·Shamik Gupta·V. K. Chandrasekar

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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.

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M. Manoranjani, Shamik Gupta, V. K. Chandrasekar. 2021-08-10. The Sakaguchi-Kuramoto model in presence of asymmetric interactions that break phase-shift symmetry. https://doi.org/10.1063/5.0055664

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