Asymmetry in the Basin Stability of Oscillation Death States under Variation of Environment-Oscillator Links

Abstract

We explore the effect of a common external system, which may be considered as a common environment, on the oscillation death(OD) states of a group of Stuart-Landau(SL) oscillators. It was found in Chaurasia et al. (Phys Rev E 98:032223, 2018), that the group of oscillators, when uncoupled to the common environment, yield a completely symmetric oscillation death state, i.e. there is an equal probability of occurrence of positive and negative oscillation death states. However, remarkably, this symmetry is significantly broken, when coupled to a common external system. For exponentially decaying common environment, the symmetry breaking of the OD states was found to be very pronounced for low environmental damping and strong oscillator-environment coupling. Here we consider the effect of disconnections of the oscillator-environment links on this asymmetry in the basin stability of the OD states. Interestingly, we find that the asymmetry induced by environmental coupling decreases with increase in fraction of such disconnections, and at some intermediate fraction close to half the symmetry is restored. However, further increase in disconnections induces asymmetry in the OD state again, until all oscillator-environment links are switched off. This suggests that a balance of on-off oscillator-environment links restores the symmetry of the OD state, and when half of the environmental connections are switched off one obtains the positive and negative OD states with almost equal probability.