| Contents |
| 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 II: Stability. |
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