Bifurcation in a predator-prey model with diffusion: Rotating waves

Abstract

This paper treats the conditions for the existence of rotating wave solutions of the CF-system modelling predator-prey interactions. It is assumed that both prey and predator are continuously distributed throughout a bounded two-dimension spatial domain of two types (unit disc and annulus), across whose boundaries there is no migration, and which simultaneously undergo simple (Fickian) diffusion. It will be shown that at a critical value of a system-parameter bifurcation takes place: a rotating wave solution arises.