A model of a myelinated nerve axon: threshold behaviour and propagation |
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Authors: | P Grindrod B D Sleeman |
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Institution: | (1) Department of Mathematical Sciences, University of Dundee, DD1 4HN Dundee, UK;(2) Present address: Mathematical Institute, University of Oxford, Oxford, UK |
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Abstract: | A model of a myelinated nerve axon is developed on the basis of FitzHugh-Nagumo dynamics under the assumption that the nodes of Ranvier are of small but finite width. It is shown that a periodic excited state may not exist if the width of the nodes is too small and the leakage across the myelin sheath is too great. The propagation of a super threshold pulse is prevented in the absence of nodes. Global stability of the resting equilibrium state is investigated as well as the propagation of wave front, type solutions. |
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Keywords: | Myelinated nerve axons Nodes of Ranvier FitzHugh-Nagumo dynamics Threshold behaviour Global stability Wave fronts |
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