Related Experiment Video
Updated: Jan 25, 2026

Stochastic Noise Application for the Assessment of Medial Vestibular Nucleus Neuron Sensitivity In Vitro
Published on: August 28, 2019
The stochastic Fitzhugh-Nagumo neuron model in the excitable regime embeds a leaky integrate-and-fire model
Marius E Yamakou1, Tat Dat Tran2, Luu Hoang Duc1,3
1Max Planck Institute for Mathematics in the Sciences, Inselstraße 22, 04103, Leipzig, Germany.
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 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.
Related Concept Videos
Leaky Scanning
Growth Models with Integration: Problem Solving
The Bohr Model
Molecular Models
The Fluid Mosaic Model
The Quantum-Mechanical Model of an Atom

