Chaotic wakes and other wave-induced behavior in a system of reaction-diffusion equations

The phenomenon of spatiotemporal chaos as it arises in systems of reaction-diffusion equations has been the subject of much study over recent years. Initially, chaotic responses in these systems were found to occur when the ratio of the diffusion coefficients was chosen sufficiently large (greater than one). Subsequently, such behavior has also been found when this ratio is taken to be unity with the conclusion that this represents a new mechanism for inducing chaos. In this paper we discuss numerical simulations of a system of reaction-diffusion equations which has been derived to study the large-scale growth patterns of fungal colonies. We show that, for this reaction-diffusion system at least, these apparently different mechanisms represent two ways of entering the same "chaotic region" in parameter space. We also discuss other wave-induced behavior which characterize the routes to chaos.