Conjugate coupling induced symmetry breaking and quenched oscillations

TL;DR

This paper explores how conjugate coupling in Stuart-Landau oscillators induces spontaneous symmetry breaking, oscillation quenching, and multistability, with analytical stability analysis and the influence of feedback factors.

Contribution

It demonstrates the emergence of symmetry breaking states through conjugate coupling and analyzes the effects of feedback on various oscillatory and quenching states.

Findings

Symmetry breaking state coexists with other dynamical states.

Decreasing feedback suppresses symmetry breaking and oscillation death.

Feedback selectively affects certain oscillation states without impacting others.

Abstract

Spontaneous symmetry breaking (SSB) is essential and plays a vital role many natural phenomena, including the formation of Turing pattern in organisms and complex patterns in brain dynamics. In this work, we investigate whether a set of coupled Stuart-Landau oscillators can exhibit spontaneous symmetry breaking when the oscillators are interacting through dissimilar variables or conjugate coupling. We find the emergence of SSB state with coexisting distinct dynamical states in the parametric space and show how the system transits from symmetry breaking state to out-of-phase synchronized (OPS) state while admitting multistabilities among the dynamical states. Further, we also investigate the effect of feedback factor on SSB as well as oscillation quenching states and we point out that the decreasing feedback factor completely suppresses SSB and oscillation death states. Interestingly, we also find the feedback factor completely diminishes only symmetry breaking oscillation and oscillation death (OD) states but it does not affect the nontrivial amplitude death (NAD) state. Finally, we have deduced the analytical stability conditions for in-phase and out-of-phase oscillations, as well as amplitude and oscillation death states.