Report
Averaging for a Fully-Coupled Piecewise Deterministic Markov Process in Infinite Dimension
| العنوان: | Averaging for a Fully-Coupled Piecewise Deterministic Markov Process in Infinite Dimension |
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| المؤلفون: | Genadot, Alexandre, Thieullen, Michèle |
| سنة النشر: | 2011 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Probability, 60J25, 60J70, 60J75, 92B9, 60H30 |
| الوصف: | In this paper, we consider the generalized Hodgkin-Huxley model introduced by Austin in \cite{Austin}. 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. Comment: 23 pages, 1 figure |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/1109.6581 |
| رقم الانضمام: | edsarx.1109.6581 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |