On a Fractional Stochastic Hodgkin-Huxley Model

Laure Coutin (1) , Jean-Marc Guglielmi (2) , Nicolas Marie (3, 4)

1 IMT - Institut de Mathématiques de Toulouse UMR5219
2 Hôpital Américain de Paris
3 MODAL'X - Modélisation aléatoire de Paris X
4 ESME - ESME - École spéciale de mécanique et d'électricité

The model studied in this paper is a stochastic extension of the so-called neuron model introduced by Hodgkin and Huxley. In the sense of rough paths, the model is perturbed by a multiplicative noise driven by a fractional Brownian motion, with a vector field satisfying the viability condition of Coutin and Marie for $\mathbb R\times [0,1]^3$. An application to the modeling of the membrane potential of nerve fibers damaged by a neuropathy is provided.

Mots clés: Stochastic differential equations; Viability theorem; Hodgkin-Huxley model; Fractional Brownian motion

Domaines: Probabilités [math.PR]

Laure Coutin, Jean-Marc Guglielmi, Nicolas Marie. On a Fractional Stochastic Hodgkin-Huxley Model. International Journal of Biomathematics, 2018, 11 (5), pp.1850061. ⟨10.1142/S1793524518500614⟩. ⟨hal-01738230v2⟩