The stability of stationary fronts for a discrete nerve axon model

2007, Volume 4, Issue 1: 113-129. doi: 10.3934/mbe.2007.4.113

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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.
- bistable,
- stability,
- spatially discrete,
- perturbation.,
- reaction-diffusion,
- Evans function
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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Abstract

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.
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