Multi-species interactions with hereditary effects and spatial diffusion

Summary We study the effect of spatial diffusion on oscillatory states in arbitrary multi-species growth models having hereditary terms. We show that it is a general principle that the addition of spatial diffusion to a stable oscillatory ecological community induces a periodic diffusion wave in which the original wavenumber (or phase) evolves according to a nonlinear evolution equation of generalized Burgers' type.Supported in part by the U.S. Army Research Office (Durham) under Contract DAHC-04-68-C-0006 and by the National Science Foundation under Grant GP-32157X2