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Threshold conditions for a diffusive model of a myelinated axon

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Abstract

This paper develops and uses comparison principles to study the time evolution of solutions to problems of the form

$$\begin{gathered} v_t = v_{xx} - gv,{\text{ for }}x \in \mathbb{R}\backslash \mathbb{Z}{\text{ (}}g{\text{ = constant),}} \hfill \\ v_t = f\left( v \right) + v_x \left( {n + ,t} \right) - v_x \left( {n - ,t} \right),{\text{ for }}x = n \in \mathbb{Z} \hfill \\ \end{gathered} $$

. Such a system models an infinite myelinated axon with discrete, excitable nodes spaced unit distant apart.

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Authors and Affiliations

  1. Mathematics Department, Suny at Buffalo, 14214, Buffalo, NY, USA

    J. Bell

  2. Mathematics Department, University of Miami, 33124, Coral Gables, FL, USA

    C. Cosner

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  1. J. Bell
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  2. C. Cosner
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Partially supported by NSF grant MCS-8101666

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Bell, J., Cosner, C. Threshold conditions for a diffusive model of a myelinated axon. J. Math. Biology 18, 39–52 (1983). https://doi.org/10.1007/BF00275909

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  • DOI: https://doi.org/10.1007/BF00275909

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