Many significant phenomenon like Synchronisation, suppression of oscillation are observed in coupled nonlinear dynamical systems. Here I investigate on two diffusively coupled FitzHugh-Nagumo system (which are in self sustained periodic firing mode), in presence of environment coupling and notice they collectively transit to amplitude death states from oscillatory states. By controlling the coupling parameters the coupled system goes to amplitude death state through inverse Hopf bifurcation.

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... nsition from oscillation to amplitude death state in different parametric zone(two-parameter space) is studied here. Though direct-indirect coupling is general methode of inducing amplitude death but this Study shows depending on parametric condition the system can revive its oscillatory states. Theoretical linear stability analysis and numerical results for different transition scenarios in different paranetric zone agree with each other. The route of transition between oscillation and amplitude death state is studied through bifurcation plot using XPPAUT AUTO package.