Transition among oscillation death, amplitude death, and revival of oscillation in coupled time-delayed systems with diffusivity and common environment

In this paper, we study the transition between different oscillation suppression, revival of oscillation, and oscillatory states in time-delayed chaotic oscillators coupled through simultaneous diffusive and environmental coupling. The present paper, for the first time, reports the occurrence of oscillation death and nontrivial amplitude death states in coupled intrinsic time-delayed systems. Moreover, we explore the revival of the oscillations from these diverse oscillation suppression states. We analyze the stability of the coupled time- delayed system and through extensive numerical investigations, we delineate all the dynamical states in the parameter space. The study is extended to a network of time-delayed oscillators and identical transition scenarios have been obtained. Finally, we support our results in an electronic hardware circuit-based experiment and demonstrate that all the transition scenarios are robust enough in a real world system where the presence of noise, fluctuations, and parameter mismatch are inevitable.