Abstract
The present paper deals with a mathematical model of a myelinated nerve axon, where nodes of Ranvier are assumed to have a finite longitudinal length. The myelinated axon contains an electrically passive part wrapped in a lipoprotein sheath. After showing the unique existence of solution and a comparison theorem, we study the propagation of excited state and its failure in the case where the passive part consists of a single segment, by adopting a coupling coefficientd as a parameter,d=1/(RL 2) with the resistanceR per unit length of axoplasm and the lengthL of segment. It is shown that there existsd *>0 such that the propagation succeeds ifd>d *, but fails ifd<d *. Regions of attraction of stable steady states are also given, and some of these results are applied to general cases.
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