Dynamical behavior of simplified FitzHugh-Nagumo neural system driven by Lévy noise and Gaussian white noise

Abstract In this paper, the dynamical behavior of simplified FitzHugh-Nagumo (FHN) neuron system under the co-excitation of Levy noise and Gaussian white noise are studied. Consideration from two aspects: the mean first-passage time (MFPT) and the probability density function (PDF) of the first-passage time (FPT). Using Janicki–Weron algorithm to generate Levy noise, and through the fourth-order Runge–Kutta algorithm to simulate the system response, the FPT of the 2 × 10 4 response tracks are calculated, and then the MFPT and the PDF are obtained. Finally, the effects of the multiplicative Gaussian noise and additive Levy noise on the MFPT and PDF of the FPT are discussed. In addition, it is found that the noise enhanced stability (NES) and resonance activation (RA) phenomena in the system.