Стохастические режимы вблизи бифуркации Лукьянова-Шильникова в модели нейрона

Abstract

We study the neuron model with the Lukyanov-Shilnikov bifurcation. Due to this bifurcation the system exhibits the coexistence of two limit cycles representing tonic spiking and bursting oscillations. We show that in the corresponding stochastic system, noise-induced transitions between the coexisting attractors can occur. We analyze this phenomenon by means of direct numerical simulations and the stochastic sensitivity functions method.