Relations between continuous and discrete models of excitable media

Abstract

The authors derived a general eikonal equation describing the evolution of a wavefront propagating in an excitable medium this equation implements the relation between the propagation speed and the wavefront curvature known from a more detailed theory. The authors used an approximate solution to obtain equations linking the excitation time scale /spl tau/ and diffusion constant D of a continuous reaction rate model with the excitation parameters of a discrete cellular automaton model on a randomized lattice.