The stochastic Fitzhugh–Nagumo neuron model in the excitable regime embeds a leaky integrate-and-fire model
In this paper, we provide a complete mathematical construction for a stochastic leaky-integrate-and-fire model (LIF) mimicking the interspike interval (ISI) statistics of a stochastic FitzHugh–Nagumo neuron model (FHN) in the excitable regime, where the unique fixed point is stable. Under specific t...
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Veröffentlicht in: | Journal of mathematical biology 2019-07, Vol.79 (2), p.509-532 |
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Format: | Artikel |
Sprache: | eng |
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Zusammenfassung: | In this paper, we provide a complete mathematical construction for a stochastic leaky-integrate-and-fire model (LIF) mimicking the interspike interval (ISI) statistics of a stochastic FitzHugh–Nagumo neuron model (FHN) in the excitable regime, where the unique fixed point is stable. Under specific types of noises, we prove that there exists a global random attractor for the stochastic FHN system. The linearization method is then applied to estimate the firing time and to derive the associated radial equation representing a LIF equation. This result confirms the previous prediction in Ditlevsen and Greenwood (J Math Biol 67(2):239–259,
2013
) for the Morris-Lecar neuron model in the bistability regime consisting of a stable fixed point and a stable limit cycle. |
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ISSN: | 0303-6812 1432-1416 |
DOI: | 10.1007/s00285-019-01366-z |