Coexisting coherent and incoherent domains near saddle-node bifurcation

A common external forcing can cause a saddle-node bifurcation in an ensemble of identical Duffing oscillators by breaking the symmetry of the individual bistable (double-well) unit. The strength of the forcing determines the separation between the saddle and the node, which in turn dictates different dynamical transitions depending on the distribution of the initial states of the oscillators. In particular, chimera-like states appear in the vicinity of the saddle-node bifurcation for which theoretical explanation is provided from the stability of the steady state of the slow-scale dynamics of the original system of equations. Further, we have also established similar states by replacing the external forcing with an appropriate coupling between the oscillators in the same parameter space. Additionally, we have also designed an appropriate coupling that can lead to saddle-node bifurcation due to symmetry breaking of the bistable systems in the vicinity of which the synchronized and desynchronized domains coexist.