Noise-induced bursting and chaos in the two-dimensional Rulkov model

Abstract

We study an effect of random disturbances on the discrete two-dimensional Rulkov neuron model. We show that close to the Neimark–Sacker bifurcation, the increasing noise can cause the transition from the noisy quiescence with small-amplitude oscillations near the stable equilibria to the stochastic bursting with large-amplitude spikes. Mean values and variations of the interspike intervals are studied in dependence of the noise intensity. To study the noise-induced bursting, the analytical approach based on the stochastic sensitivity functions technique and confidence ellipses method is applied. On the basis of the largest Lyapunov exponents, we show how the noise-induced transition from the quiescence to stochastic bursting regime is accompanied by the transformation of dynamics from regular to chaotic.