In this paper, we investigate the emergence of a ratio-dependent predator-prey system with Michaelis-Menten–type functional response and reaction diffusion. We obtain the conditions of Hopf, Turing, and wave bifurcation in a spatial domain. Furthermore, we present a theoretical analysis of evolutionary processes that involves organisms distribution and their interaction of spatially distributed population with local diffusion. The results of numerical simulations reveal that the typical dynamics of population density variation is the formation of isolated groups, i.e., stripelike or spotted or coexistence of both. Our study shows that the spatially extended model has not only more complex dynamic patterns in the space, but also chaos and spiral waves. It may help us better understand the dynamics of an aquatic community in a real marine environment.

• Received 6 January 2007

DOI:https://doi.org/10.1103/PhysRevE.75.051913