Transitions among the diverse oscillation quenching states induced by the interplay of direct and indirect coupling

Abstract: We report the transitions among different oscillation quenching states induced by the interplay of diffusive (direct) coupling and environmental (indirect) coupling in coupled identical oscillators. This coupling scheme was introduced by Resmi {\it et al}. [Phys. Rev. E, 84, 046212 (2011)] as a general scheme to induce amplitude death (AD) in nonlinear oscillators. Using a detailed bifurcation analysis we show that in addition to AD, which actually occurs only in a small region of parameter space, this coupling scheme can induce other oscillation quenching states, namely oscillation death (OD) and a novel nontrvial AD (NAD) state, which is a nonzero {\it bistable} homogeneous steady state; more importantly, this coupling mediates a transition from AD to OD state and a new transition from AD to NAD state. We identify diverse routes to the NAD state and map all the transition scenarios in the parameter space for periodic oscillators. Finally, we present the first experimental evidence of oscillation quenching states and their transitions induced by the interplay of direct and indirect coupling.