Non-Gaussian noise induced stochastic resonance in FitzHugh–Nagumo neural system with time delay

Shenghong Li,Jiwei Huang

doi:10.1063/1.5118730

Abstract

In this paper, non-Gaussian noise induced stochastic resonance for the FitzHugh–Nagumo neural system with a time delay is investigated. Through the path integral method, the non-Gaussian noise is approximated as a colored noise, and according to the unified colored noise theory and the method of probability density approximation, a stochastic differential equation with a Markovian property is obtained. Then, by applying the two-state theory, the expression of the signal-to-noise ratio (SNR) is derived. Finally, the effects of non-Gaussian noise and time delay parameters in the neural system on the SNR are discussed with the help of analytical results.

Highlights

Stochastic resonance was first presented to investigate the quaternary glacial problem,1,2 and its existence was found in the experiment of the Schmitt trigger circuit system by Fauve.3 Because stochastic resonance illustrates the beneficial aspect of noise, great attention was paid
The fact that the existence of time delay makes stochastic systems non-Markovian leads to difficulty in obtaining analytical results, so some approximation methods have been used to obtain analytical expressions
Frank presented that the Novikov theorem could still facilitate a stochastic time-delay system, which is given in Refs. 20–22, and the equivalent Itô stochastic differential equation to the original system was obtained by probability density approximation

Summary

INTRODUCTION

Stochastic resonance was first presented to investigate the quaternary glacial problem, and its existence was found in the experiment of the Schmitt trigger circuit system by Fauve. Because stochastic resonance illustrates the beneficial aspect of noise, great attention was paid. Time delay exists extensively and has an important influence on the behavior of stochastic nonlinear dynamical systems. The fact that the existence of time delay makes stochastic systems non-Markovian leads to difficulty in obtaining analytical results, so some approximation methods have been used to obtain analytical expressions. The approximation of little time delay was proposed and the stationary probability density solution of a stochastic system via this method was derived by Guillouzi.. 20–22, and the equivalent Itô stochastic differential equation to the original system was obtained by probability density approximation. In this paper, non-Gaussian noise induced stochastic resonance in the FitzHugh–Nagumo neural system with a time delay is studied..

FitzHugh–Nagumo NEURAL SYSTEM

APPROXIMATION OF NON-GAUSSIAN NOISE AND TIME DELAY

STOCHASTIC RESONANCE AND NUMERICAL RESULTS

CONCLUSION