Abstract
The FitzHugh-Nagumo equation u t =u xx +f(u)-w, u t =b(u-dw), is a simplified mathematical description of a nerve axon. If the parameters b>0 and d⩾0 are taken suitably, this equation has two travelling pulse solutions with different propagation speeds. We study the stability of the fast pulse solution when b>0 is sufficiently small. It is proved analytically by eigenvalue analysis that the fast pulse solution is “exponentially stable” if d>0, and is “marginally stable” but not exponentially stable if d=0.
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