Spontaneous symmetry breaking (SSB) is essential and plays a vital role many natural phenomena, including 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.

The phenomenon of spontaneous symmetry breaking facilitates the onset of a plethora of nontrivial dynamical states/patterns in a wide variety of dynamical systems. Spontaneous symmetry breaking results in amplitude and phase variations in a coupled identical oscillator due to the breaking of the prevailing permutational/translational symmetry of the coupled system. Nevertheless, the role and the competing interaction of the low-pass filter and the mean-field density parameter on the symmetry breaking dynamical states are unclear and yet to be explored explicitly. The effect of low pass filtering along with the mean-field parameter is explored in conjugately coupled Stuart–Landau oscillators. The dynamical transitions are examined via bifurcation analysis. We show the emergence of a spontaneous symmetry breaking (asymmetric) oscillatory state, which coexists with a nontrivial amplitude death state. Through the basin of attraction, the multi-stable nature of the spontaneous symmetry breaking state is examined, which reveals that the asymmetric distribution of the initial state favors the spontaneous symmetry breaking dynamics, while the symmetric distribution of initial states gives rise to the nontrivial amplitude death state. In addition, the trade-off between the cut-off frequency of the low-pass filter along with the mean-field density induces and enhances the symmetry breaking dynamical states. Global dynamical transitions are discussed as a function of various system parameters. Analytical stability curves corresponding to the nontrivial amplitude death and oscillation death states are deduced.

We investigate the effect of symmetry breaking couplings on the macroscopic dynamical behavior of an ensemble of globally coupled active and inactive oscillators. Conjugate coupling among the ensemble and the weighted coupling within the active and inactive groups introduces the asymmetry. Large values of the global coupling strength facilitate the onset of the phenomenon of aging transition, thereby deteriorating the macroscopic oscillatory behavior. We find that the natural frequency of oscillation favors the onset of the aging transition even in the presence of a large proportion of the active oscillators because of the broken symmetry. Further the ratio of the intra-group (weighted) couplings plays a nontrivial role in determining the dynamical behaviors and their transitions. It is also observed that even a feeble change in the simple feedback factor in the coupling facilitates the counterintuitive effect of preserving the macroscopic oscillatory nature of the ensemble, comprising completely inactive oscillators, in the entire parameter space where the ensemble suffered the aging transition.