Conjugate coupling-induced spontaneous symmetry breaking (Vol. 50, No. 1)

Spontaneous symmetry breaking (SSB) is a phenomenon that can facilitate the onset of a rich variety of complex patterns observed in several natural systems. In SSB, asymmetric states arise from symmetric systems spontaneously as a control parameter is varied. This study reveals the existence of spontaneous symmetry breaking state induced by conjugate coupling which corresponds to coupling in paradigmatic Stuart-Landau oscillators. The system exhibits distinct dynamical states, namely in-phase synchronized (IPS), out-of-phase synchronized (OPS), nontrivial amplitude death (NAD) and oscillation death (OD) states. We have deduced the explicit analytical solutions of these states and have studied their stability. The system also exhibits multistabilities among the dynamical states including IPS-OPS (R1), OPS-NAD (R2), SSB-NAD (R3), NAD-OD (R4) and SSB-NAD-OPS (R5). It is known that feedback is a useful control mechanism in many biological systems. While introducing the feedback factor in a conjugately coupled system it completely suppresses the SSB and OD states but does not influence the NAD state. These results will shed light on the dynamics of SSB and the control of such dynamical states.

K. Ponrasu, K. Sathiyadevi, V. K. Chandrasekar and M. Lakshmanan, Conjugate coupling-induced symmetry breaking and quenched oscillations, EPL 124, 20007 (2018)
[Abstract]