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

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. Sakaguchi-Kuramoto is a generalization of the basic that considers presence phase-lag parameter in interaction, thereby making it asymmetric between oscillator pairs. Here, we consider further generalization, by adding interaction breaks phase-shift symmetry model. highlight our unveiling very rich bifurcation diagram comprising both oscillatory non-oscillatory synchronized states as well incoherent state: There are regions two-state interesting hitherto unexplored three-state coexistence arising from interactions