The study on dynamical behavior of FitzHugh–Nagumo neural model under the co-excitation of non-Gaussian and colored noise

Abstract

The dynamical behavior of the one-dimensional FitzHugh–Nagumo (FN) neural model under the co-excitation of cross-correlation multiplicative non-Gaussian noise and additive colored noise are investigated in this paper. Firstly, the one-dimensional Langevin equation of the FN model can be obtained by using the adiabatic elimination method. Then, the approximate Fokker–Planck equation (AFPE) is derived with functional methods, and the expressions of steady-state probability density function (PDF) and the mean first-passage time (MFPT) are obtained. Finally, the effects of different parameters on PDF and MFPT are discussed as a reflection of the properties of the FN neural model. Moreover, under certain conditions, noise enhanced stability (NES) effects can be induced by noise.