Quenching and restoration of oscillations under environmental interactions

Different types of collective dynamical behavior of the coupled oscillator networks are investigated under heterogeneous environmental coupling. This type of interaction pattern mainly occurs indirectly between two or more dynamical units. By interplaying the diffusive and the environmental coupling, the transition scenarios among several collective states, such as complete synchronization, amplitude, and oscillation death are explored in the coupled dynamical network. Here we consider a heterogeneous environmental coupling scheme, meaning that two or more dynamical units are not only connected via one medium but they can rely on their information through more than one medium. Another type of heterogeneity is introduced in terms of the coupling asymmetry in the interacting network structure and it is observed that the proper tuning of the coupling heterogeneity parameter is capable of restoring the dynamic rhythm from the oscillation suppressed state. Using detailed bifurcation analysis it is shown that the asymmetry parameter plays a key role in the transition among the several collective dynamical states and we map them in the different parameter space. We analytically derived the stability conditions for the existence of different dynamical states. The analytical findings are confirmed by numerical results. We performed the numerical simulation on networks of Stuart-Landau oscillators. Finally, we extend this investigation to large network sizes. In this case, we observe the novel transitions from amplitude death to multicluster oscillation death states and correspondingly, the revival of oscillations from the different suppressed states is also articulated.