Stochastic FitzHugh-Nagumo neuron model in excitable regime embeds a leaky integrate-and-fire model
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.
Keywords
Cite
@article{arxiv.1806.07149,
title = {Stochastic FitzHugh-Nagumo neuron model in excitable regime embeds a leaky integrate-and-fire model},
author = {Marius E. Yamakou and Tat Dat Tran and Luu Hoang Duc and Juergen Jost},
journal= {arXiv preprint arXiv:1806.07149},
year = {2019}
}
Comments
15 pages, 7 figures, 1 table. arXiv admin note: text overlap with arXiv:1108.0073 by other authors