WAVE-PROPAGATION AND CURVATURE EFFECTS IN A MODEL OF EXCITABLE MEDIA

This paper presents a theory of planar and curved front propagation in a simple model of excitable media based on a diffusion mechanism. It uses the diffusion coefficient along with space and time constants to model propagation. The model allows for analytical computation of planar wave speed as well as curvature relations (speed c vs curvature K of front) in the continuum limit, including a determination of the critical curvature at which propagation fails, K-cr. It is shown that the model exhibits a lower bound for the propagation speed related to the space and time constants, and compute unstable solutions in the planar and curved wave cases. The theoretical results are compared with numerical simulations of a discrete-space/continuous-time version of the model and with similar results in reaction-diffusion equations.