Cross-diffusion predator–prey model derived from the dichotomy between two behavioral predator states

Cross-diffusion may be an important driving force of pattern formation in population models. Recently, a relation between cross-diffusion and reaction-diffusion systems has been revealed from the mathematical modeling point view. In this paper, we derive predator–prey model with simple system two behavioral states predator examine whether can induce spatial patterns We assume that predators have identical characteristics except for their mobility searching activity preys: consider states, namely less mobile preys more actively than predators. Our analysis shows derived situation if prey-density-dependent conversion rate state to one increases rapidly at high prey density.