Stability of fast travelling pulse solutions of the FitzHugh—Nagumo equations
The FitzHugh-Nagumo equation ut=uxx+f(u)-w, ut=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.