Generic excitable dynamics on a two-dimensional map

This paper introduces a two-dimensional map exhibiting several generic properties reported in excitable systems. The elementary dynamic that is analogous to that of neural elements, is analyzed using phase plane methods. Bifurcations from nonautonomous to autonomous, and from periodic to chaotic solutions are studied in a small region of parameter space. The basic implementation of distributed excitable networks using coupled maps lattices is described in one- and two-dimensional media with nearest-neighbor coupling.