Effect of diffusion on patterns in excitable Belousov-Zhabotinskii systems

Travelling wave patterns occur frequently in chemically reacting systems; these include planar fronts, target patterns and spiral structures. We review the dispersion relation for planar waves, including the effects of diffusion in the "slow" field for a simplified piecewise-linear model, with a focus on the scaling behavior with respect to the relative rate of the "fast" and "slow" reactions. We discuss the implications of these results for spirals, showing the origins of Fife scaling and deriving a boundary-integral formulation of the spiral equations. We discuss the generalization to more realistic models, in particular, the popular Oregonator model for Belousov-Zhabotinskii reactions.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/27721/1/0000109.pd