Spatial pattern formation of a ratio-dependent predator–prey model

This paper presents a theoretical analysis of evolutionary process that involves organisms distribution and their interaction of spatially distributed population with diffusion in a Holling-III ratio-dependent predator–prey model, the sufficient conditions for diffusion-driven instability with Neumann boundary conditions are obtained. Furthermore, it presents novel numerical evidence of time evolution of patterns controlled by diffusion in the model, and finds that the model dynamics exhibits complex pattern replication, and the pattern formation depends on the choice of the initial conditions. The ideas in this paper may provide a better understanding of the pattern formation in ecosystems.