Probability Density Transitions in the FitzHugh-Nagumo Model with Lévy Noise
Xu Yong, Feng Jing, Xu Wei and Gu Rencai

doi:10.3970/cmes.2015.106.309
Source CMES: Computer Modeling in Engineering & Sciences, Vol. 106, No. 5, pp. 309-322, 2015
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Keywords Lévy noise, FitzHugh-Nagumo model, firing time, stochastic bifurcation, stationary probability density, mean first passage time.
Abstract

In this paper, bifurcation analysis and numerical simulations are performed on the FitzHugh-Nagumo system in the presence of Lévy stable noise. The stationary probability density functions are obtained to examine the influences of noise intensity and stability index. Results show that under the influences of noise intensity and stability index, the dynamic of the FitzHugh-Nagumo model can be well characterized through the concept of stochastic bifurcation, consisting in qualitative changes of the stationary probability distribution. Then, the mean passage time between the resting and action state is investigated as functions of noise intensity and stability index of the external signal by means of numerical simulations. Dependences of the results on the parameters of Lévy noise are discussed to find the different mechanisms compared with Gaussian case.

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