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.
This is the published version, also available here: http://dx.doi.org/10.1137/S003613990343687X.
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