Conjugate coupling-induced symmetry breaking and quenched oscillations

¹ Centre for Nonlinear Science & Engineering, School of Electrical & Electronics Engineering, SASTRA Deemed University - Thanjavur-613 401, Tamil Nadu, India
² Centre for Nonlinear Dynamics, School of Physics, Bharathidasan University Tiruchirappalli-620 024, Tamil Nadu, India

Received: 10 September 2018
Accepted: 23 October 2018

Abstract

Spontaneous symmetry breaking (SSB) is essential and plays a vital role in many natural phenomena, including the formation of the 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 the 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 the 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 that 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.