  We consider the singularly perturbed limit of periodically excited
two-dimensional FitzHugh-Nagumo systems. We show that the dynamics of such
systems are essentially governed by an one-dimensional map and present a
numerical scheme to accurately compute it together with its Lyapunov exponent.
We then investigate the occurrence of chaos by varying the parameters of the
system, with especial emphasis on the simplest possible chaotic oscillations.
Our results corroborate and complement some recent works on bifurcations and
routes to chaos in certain particular cases corresponding to piecewise linear
FitzHugh-Nagumo-like systems.
