Stability analysis of predator–prey models involving cross-diffusion

Abstract

Abstract In this paper we have considered a three dimensional system of partial differential equations to model the dynamical interactions of two predators competing for a single prey. The model is developed by introducing cross diffusion in such a way as to take into account the migratory strategy adopted by the predators, who take advantage of the defense switching behavior of the prey. Equilibria of the model are determined and a local stability analysis is discussed. The main result presented here is that for certain range of values of the cross diffusion parameters, the system has a continuum of equilibria and a zip-type bifurcation occurs and this is not sustainable due to the emergence of Turing type instability.