D. Ambrosi, G. Arioli, H. Koch A homoclinic solution for excitation waves on a contractile substratum (137K, tex) ABSTRACT. We analyze a model of electric signalling in biological tissues and prove that this model admits a travelling wave solution. Our result is based on a new technique for computing rigorous bounds on the stable and unstable manifolds at an equilibrium point of a dynamical system depending on a parameter.