Complex patterns in a predator-prey model with self and cross-diffusion

In this paper we present a theoretical analysis of processes of pattern formation that Involves organisms distribution and their interaction of spatially distributed population with self as well as cross diffusion in a Beddington-DeAngelis type predator-prey model The instability of the uniform equilibrium of the model is discussed and the sufficient conditions for the instability with zero-flux boundary conditions are obtained Furthermore we present novel numerical evidence of time evolution of patterns controlled by self as well as cross-diffusion in the model and find that the model dynamics exhibits a cross diffusion controlled formation growth not only to stripes-spots but also to hot/cold spots stripes and wave pattern replication This may enrich the pattern formation in cross-diffusive predator-prey model (C) 2010 Elsevier B V All rights reserved