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We report the transitions among different oscillation quenching statesinduced by the interplay of diffusive (direct) coupling and environmental(indirect) coupling in coupled identical oscillators. This coupling scheme wasintroduced by Resmi {\it et al}. [Phys. Rev. E, 84, 046212 (2011)] as a generalscheme to induce amplitude death (AD) in nonlinear oscillators. Using adetailed bifurcation analysis we show that in addition to AD, which actuallyoccurs only in a small region of parameter space, this coupling scheme caninduce other oscillation quenching states, namely oscillation death (OD) and anovel nontrvial AD (NAD) state, which is a nonzero {\it bistable} homogeneoussteady state; more importantly, this coupling mediates a transition from AD toOD state and a new transition from AD to NAD state. We identify diverse routesto the NAD state and map all the transition scenarios in the parameter spacefor periodic oscillators. Finally, we present the first experimental evidenceof oscillation quenching states and their transitions induced by the interplayof direct and indirect coupling.

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