Infinite multiplicity and separation structure of positive solutions for a semilinear elliptic equation in Rn

In this paper, we study a strongly coupled system of partial differential equations which models the dynamics of a two-predator-one-prey ecosystem in which the prey exercises a defense switching mechanism and the predators collaboratively take advantage of the preyʹs strategy. We demonstrate the emergence of stationary patterns for this system, and show that it is due to the cross diffusion that arises naturally in the model. As far as the authors are aware, this is the first example of stationary patterns in a predator–prey system arising solely from the effect of cross diffusion.