Existence of wavefronts and impulses to FitzHugh–Nagumo equations Original Research Article

Consideration is given to the FitzHugh–Nagumo equations ut=uxx−f(u)−v,vt=ε(u−γv), where f(u)=u(u−1)(u−a), 00,γ>9/((1−2a)(2−a)). It is shown that there exist some co>0 so that the system has a heteroclinic travelling wave solution with wave speed co for any ε>0, and there exists coo∈(0,co), such that (1.2) has a homoclinic solution with wave speed coo if and only if εγ2<1.