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Mathematical Biosciences and Engineering

2007, Volume 4, Issue 1: 113-129. doi: 10.3934/mbe.2007.4.113
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The stability of stationary fronts for a discrete nerve axon model

  • 1.
    High Bridge, NJ 08829
  • Received: 01 April 2006 Accepted: 29 June 2018 Published: 01 November 2006

  • MSC : 34K20,37K45.

  • We consider the stability of single-front stationary solutions to a spatially discrete reaction-diffusion equation which models front propagation in a nerve axon. The solution's stability depends on the coupling parameter, changing from stable to unstable and from unstable to stable at a countably infinite number of values of this diffusion coefficient.

    Citation: Christopher E. Elmer. The stability of stationary fronts for a discrete nerve axon model[J]. Mathematical Biosciences and Engineering, 2007, 4(1): 113-129. doi: 10.3934/mbe.2007.4.113

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  • We consider the stability of single-front stationary solutions to a spatially discrete reaction-diffusion equation which models front propagation in a nerve axon. The solution's stability depends on the coupling parameter, changing from stable to unstable and from unstable to stable at a countably infinite number of values of this diffusion coefficient.


  • This article has been cited by:

    1. Elizabeth Lydon, Brian E. Moore, Propagation failure of fronts in discrete inhomogeneous media with a sawtooth nonlinearity, 2016, 22, 1023-6198, 1930, 10.1080/10236198.2016.1255209
    2. Brian E. Moore, Joseph M. Segal, Stationary bistable pulses in discrete inhomogeneous media, 2014, 20, 1023-6198, 1, 10.1080/10236198.2013.800868
    3. A. R. Humphries, Brian E. Moore, Erik S. Van Vleck, Front Solutions for Bistable Differential-Difference Equations with Inhomogeneous Diffusion, 2011, 71, 0036-1399, 1374, 10.1137/100807156
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  • © 2007 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
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  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

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