期刊
JOURNAL OF MATHEMATICAL BIOLOGY
卷 79, 期 2, 页码 509-532出版社
SPRINGER HEIDELBERG
DOI: 10.1007/s00285-019-01366-z
关键词
FitzHugh-Nagumo model; Excitable regime; Leaky integrate-and-fire model; Random attractor; Stationary distribution
资金
- Max Planck Society
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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