We deal with the singularly perturbed Nagumo-type equation where ε > 0 is a real parameter and a : R -> R is a piecewise constant function satisfying 0 < a(s) < 1 for all s. For small ε, we prove the existence of chaotic, homoclinic and heteroclinic solutions. We use a dynamical systems approach, based on the Stretching Along Paths technique and on the Conley–Wazewski's method.
