American Institute of Mathematical Sciences

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2007, 4(1): 113-129. doi: 10.3934/mbe.2007.4.113

The stability of stationary fronts for a discrete nerve axon model

Christopher E. Elmer 1,

1. 

High Bridge, NJ 08829, United States

Received  April 2006 Revised  August 2006 Published  November 2006

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.
Keywords: bistable, stability, spatially discrete, perturbation., reaction-diffusion, Evans function.
Mathematics Subject Classification: 34K20,37K4.
Citation: Christopher E. Elmer. The stability of stationary fronts for a discrete nerve axon model. Mathematical Biosciences & Engineering, 2007, 4 (1) : 113-129. doi: 10.3934/mbe.2007.4.113
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