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Spatially Discrete FitzHugh-Nagumo Equations
Elmer, Christopher E. Van Vleck, Erik S.
Elmer, Christopher E.
Van Vleck, Erik S.
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Abstract
We consider pulse and front solutions to a spatially discrete FitzHugh--Nagumo equation that contains terms to represent both depolarization and hyperpolarization of the nerve axon. We demonstrate a technique for deriving candidate solutions for the McKean nonlinearity and present and apply solvability conditions necessary for existence. Our equation contains both spatially continuous and discrete diffusion terms.
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This is the published version, also available here: http://dx.doi.org/10.1137/S003613990343687X.
Date
2005-04-05
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Society for Industrial and Applied Mathematics
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Keywords
traveling fronts and pulses, discrete diffusion
Citation
Elmer, Christopher E. & Van Vleck, Erik. "Spatially Discrete FitzHugh-Nagumo Equations." (2005) SIAM J. Appl. Math., 65(4), 1153–1174. (22 pages). http://dx.doi.org/10.1137/S003613990343687X.