Co-existence of in-phase oscillations and oscillation death in environmentally coupled limit cycle oscillators

We study the emergent dynamics of limit cycle oscillators coupled indirectly via a dynamic environment. We report the co-existence of in-phase oscillations and oscillation death in the parameter plane, which is observed for the first time in indirectly coupled systems. It is found that the emergent dynamics of this system crucially depend on both the decay parameter of the environment and the density of the mean-field coupling. Also, we found a distinct route to suppressed oscillation state, namely, amplitude death and oscillation death, from the oscillatory solutions. Our numerical results are consistent with the analytical results obtained from linear stability analysis and further corroborated by the experimental results obtained from the electronic circuit implementation of the system.