Oscillator Death in Sinusoidally Coupled Fitzhugh Nagumo Neural Oscillators

In the dynamics of sinusoidally coupled Fitzhugh Nagumo neural oscillators, when new stable, steady states are induced on limit cycles, and the symmetry is broken, it leads to Oscillator death. Also, during this process, the interacting oscillators pull each other such that both fail to be on limit cycles and hence meet Oscillator death. The present work investigates the effect of the interplay between initial conditions and coupling gain in causing Oscillator death. Two regimes have been identified to explain whether Oscillator death would occur or not. In the first regime, the initial conditions are such that there exists a finite coupling gain after the arrival of synchronization, where the Oscillator death takes place. While in the second regime, the initial conditions are such that any amount of increase in coupling gain fails to give Oscillator death. The Samle's effect, which is known as inverse of Oscillator death activity, has also been explored. It was found that the oscillations get revived in response to the reduction in coupling gain below a threshold.