2011/09/29 by Alexandre Génadot, Genadot, Alexandre, M. Thieullen +1
Biochemistry, Genetics and Molecular Biology · Physics and Astronomy · #60H30 #60J25 #60J70 #60J75 #92B9 #Diffusion and Search Dynamics #FOS: Mathematics #Gene Regulatory Network Analysis #Probability (math.PR) #stochastic dynamics and bifurcation
paper · pdf · doi:10.48550/arxiv.1109.6581
openalex publication_date 2011/09/29 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
In this paper, we consider the generalized Hodgkin-Huxley model introduced by Austin in \citeAustin. This model describes the propagation of an action potential along the axon of a neuron at the scale of ion channels. Mathematically, this model is a fully-coupled Piecewise Deterministic Markov Process (PDMP) in infinite dimension. We introduce two time scales in this model in considering that some ion channels open and close at faster jump rates than others. We perform a slow-fast analysis of this model and prove that asymptotically this two time scales model reduces to the so called averaged model which is still a PDMP in infinite dimension for which we provide effective evolution equations and jump rates.