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.Comment: Accepted for publication in Europhysics Letter
