Effect of time delay in FitzHugh–Nagumo neural model with correlations between multiplicative and additive noises

Chunhua Zeng, Chunping Zeng, Ailing Gong and Linru Nie

Physica A: Statistical Mechanics and its Applications, 2010, vol. 389, issue 22, 5117-5127

Abstract: We study the effect of time delay in the FitzHugh–Nagumo neural model with correlations between multiplicative and additive noise terms. Based on the corresponding Fokker-Planck equation, the explicit expressions of the stationary probability distribution function (SPDF), the mean first passage time (MFPT) and the signal-to-noise ratio (SNR) are obtained, respectively. Research results show that: (i) the system undergoes a succession of two phase transitions (i.e., the reentrance phenomenon) as the noise correlation parameter is increased and a (single) phase transition as the time delay is increased. (ii) The MFPT as a function of the multiplicative noise intensity exhibits a maximum. This maximum for MFPT identifies the noise enhanced stability (NES) effect, the noise correlation parameter intensifies the NES effect while the time delay, and the additive noise intensity weakens it. (iii) The existence of a maximum in the SNR as a function of the multiplicative noise intensity is the identifying characteristic of the stochastic resonance (SR) phenomenon, the noise correlation parameter enhances the SR while the time delay, and the additive noise intensity weaken it.

Keywords: Time delay; Noise correlation; FitzHugh–Nagumo neural model (search for similar items in EconPapers)
Date: 2010
References: View complete reference list from CitEc
Citations: View citations in EconPapers (5)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:389:y:2010:i:22:p:5117-5127

DOI: 10.1016/j.physa.2010.07.031

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