Transition from amplitude to oscillation death under mean-field diffusive coupling

We study the transition from amplitude death (AD) to oscillation death (OD) state in limit-cycle oscillators coupled through mean-field diffusion. We show that this coupling scheme can induce an important transition from AD to OD even in {\it identical} limit cycle oscillators. We identify a parameter region where OD and a novel {\it nontrivial} AD (NT-AD) state coexist. This NT-AD state is unique in comparison with AD owing to the fact that it is created by a subcritical pitchfork bifurcation, and parameter mismatch does not support but destroy this state. We extend our study to a network of mean-field coupled oscillators to show that the transition scenario preserves and the oscillators form a two cluster state.