  In this paper, we investigate the emergence of a ratio-dependent
predator-prey system with Michaelis-Menten-type functional response and
reaction-diffusion. We derive the conditions for Hopf, Turing and Wave
bifurcation on 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.
