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| The FitzHugh-Nagumo model is a reaction-diffusion equation describing the propagation of electrical signals nerve axons and other biological tissues. One of the model parameters is the ratio of two time scales, ranging from 1/1000 to 1/10 in typical simulations of nerve axons. Based on the existence of a (singular) limit at ratio=0, it has been shown that the FitzHugh-Nagumo equation admits a stable traveling pulse solution for sufficiently small ratio>0. In the work presented here we prove the existence and stability of such a solution for the ratio 1/100. We cover both circular axons and axons of infinite length. Our method is non-perturbative and should apply to a wide range of other parameter values.
Part I: Existence |
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