Stochastic resonance induced by Gaussian white noise and Lévy noise in simplified FitzHugh–Nagumo neural system

Abstract

This paper aims to investigate the stochastic resonance (SR) of simplified FitzHugh–Nagumo (FHN) neuron system driven by Gaussian white noise and Levy noise. The Levy noise is generated by Janicki–Weron algorithm, and the numerical solutions of system equation are obtained by the fourth-order stochastic Runge–Kutta algorithm. Then, the SR is determined by the classical measure of signal-to-noise ratio (SNR). Finally, the effects of the Gaussian white noise, Levy noise and system parameters on SNR are discussed by means of numerical simulation. The results show that the larger stability index and skewness parameter are conducive to enhance signal response of FHN neural system; on the contrary, the increase in amplitude $$ A $$ and system parameter $$ \gamma $$ weakens the occurrence of SR.