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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Grindrod, P., Sleeman, B.D. A model of a myelinated nerve axon: threshold behaviour and propagation. J. Math. Biology 23, 119–135 (1985). https://doi.org/10.1007/BF00276561
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DOI: https://doi.org/10.1007/BF00276561