Piecewise Smooth Map of Neuronal Activity: Deterministic and Stochastic Cases

Abstract

In this paper we consider a Rulkov model of the neuronal dynamics, given by a piecewise smooth discontinuous one-dimensional map with random perturbation. The purpose of this study is to analyze the possible regimes and bifurcations of the deterministic system, as well as to study the influence of external random impact on attractors of the system. Using the stochastic sensitivity function, stochastic phenomena are described, such as noise-induced transitions between attractors and noise-induced large-amplitude oscillations.