Search

MiS Preprint Repository

We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint
45/2018

Stochastic FitzHugh-Nagumo neuron model in excitable regime embeds a leaky integrate-and-fire model

Marius E. Yamakou, Tat Dat Tran, Hoang Duc Luu and Jürgen Jost

Abstract

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, S. and Greenwood, P. (2013). The Morris-Lecar neuron model embeds a leaky integrate-and-fire model. Journal of Mathematical Biology, 67(2):239-259] for the Morris-Lecar neuron model in the bistability regime consisting of a stable fixed point and a stable limit cycle.

Received:
29.06.18
Published:
11.09.18
MSC Codes:
60GXX, 92Bxx
Keywords:
FitzHugh-Nagumo model, excitable regime, leaky integrate-and-fire model, random attractor, stationary distribution

Related publications

inJournal
2019 Journal Open Access
Marius Emar Yamakou, Tat Dat Tran, Hoang Duc Luu and Jürgen Jost

The stochastic Fitzhugh-Nagumo neuron model in the excitable regime embeds a leaky integrate-and-fire model

In: Journal of mathematical biology, 79 (2019) 2, pp. 509-532