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

Author

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  • Zeng, Chunhua
  • Zeng, Chunping
  • Gong, Ailing
  • Nie, Linru

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.

Suggested Citation

  • Zeng, Chunhua & Zeng, Chunping & Gong, Ailing & Nie, Linru, 2010. "Effect of time delay in FitzHugh–Nagumo neural model with correlations between multiplicative and additive noises," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(22), pages 5117-5127.
    • Handle: RePEc:eee:phsmap:v:389:y:2010:i:22:p:5117-5127
    DOI: 10.1016/j.physa.2010.07.031
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    Citations

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    Cited by:

    1. Zeng, Chunhua & Wang, Hua, 2012. "Noise and large time delay: Accelerated catastrophic regime shifts in ecosystems," Ecological Modelling, Elsevier, vol. 233(C), pages 52-58.
    2. Wang, Min & Fang, Yuwen & Luo, Yuhui & Yang, Fengzao & Zeng, Chunhua & Duan, Wei-Long, 2019. "Influence of non-Gaussian noise on the coherent feed-forward loop with time delay," Chaos, Solitons & Fractals, Elsevier, vol. 129(C), pages 46-55.
    3. Mandal, Saroj Kumar & Poria, Swarup, 2023. "A study of Michaelis–Menten type harvesting effects on a population in stochastic environment," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 611(C).
    4. Cesar Manchein & Paulo C. Rech, 2024. "Effects of external stimuli on the dynamics of deterministic and stochastic Hindmarsh–Rose neuron models," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 97(8), pages 1-16, August.
    5. Shengli Guo & Jun Tang & Jun Ma & Chunni Wang, 2017. "Autaptic Modulation of Electrical Activity in a Network of Neuron-Coupled Astrocyte," Complexity, Hindawi, vol. 2017, pages 1-13, June.

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