First order transition to oscillation death through an environment

Abstract

The emergence of dynamical abrupt transitions for the first time in an ensemble of identical limit-cycle and chaotic oscillators coupled via a common environment is reported. The transition from the oscillatory state to the death state and vice versa, in these networks of oscillators are found not only discontinuous as well as irreversible in the parameter space. This first order phase transition in these systems is termed as Explosive Death. The occurrence of such transition is studied in details by using an appropriate order parameter for both limit-cycle and chaotic oscillators, in particular, Stuart–Landau and Rössler oscillators. The backward transition point for this phenomenon is obtained analytically using linear stability analysis and is found to be consistent with the numerical results.