Stochastic dynamics of Izhikevich-Fitzhugh neuron model

This paper is concerned with stochastic stability and stochastic bifurcation of the Fitzhug-Nagumo model with multiplicative white noise. We employ largest Lyapunov exponent and singular boundary theory to investigate local and global stochastic stability at the equilibrium point. In the rest, the solution of averaging the Ito diffusion equation and extreme point of steady-state probability density function provide sufficient conditions that the stochastic system undergoes pitchfork and phenomenological bifurcations. These theoretical results of the stochastic neuroscience model are confirmed by some numerical simulations and stochastic trajectories. Finally, we compare this approach with Rulkov approach and explain how pitchfork and phenomenological bifurcations describe spiking limit cycles and stability of neuron's resting state.

Keywords:

Stochastic systems , Izhikevich-FitzHugh model , stochastic stability , Bifurcation