Spatial Patterns for Discrete Models of Diffusion in Excitable Media

In a spatially homogeneous environment an excitable media is characterized by a globally stable equilibrium state, and also by a threshold mechanism which produces a large amplitude response to a sufficiently large stimulus. This response is temporary, however, and the system soon returns to its equilibrium configuration. Such media are to be distinguished from oscillatory ones; the latter support self-excited spatially homogeneous oscillations. In this paper we show how spatial inhomogeneities in an excitable media tend to organize themselves to produce spatial patterns which oscillate periodically in time.