Wave Propagation in Excitable Media Through Randomly Distributed Heterogeneities: Simulations and Comparison to the Effective Medium Theory

Abstract

The propagation of traveling waves in excitable media with randomly distributed diffusion coefficient is studied. If the characteristic size of the waves is much larger than the heterogeneity size an effective medium theory based on a self-consistent homogenization approach can be applied. The random distribution of the medium properties is produced by domains of two phases. In each phase the values of the diffusion coefficient are different. The characteristic size of the domains of the two phases is varied in the numerical simulations. The resulting velocities of the traveling waves found by numerical simulations of the random media are compared with the predictions of the effective medium theory. For large size of the heterogeneities in comparison with the diffusion length of the reaction-diffusion system the numerical results show deviations with respect to the predictions.