Stationary patterns for a prey–predator model with prey-dependent and ratio-dependent functional responses and diffusion

We study a reaction diffusion system arising from a three-species prey–predator model with prey-dependent and ratio-dependent functional responses. The main aim of this paper is to study the global existence and bifurcation of non-constant positive steady-states. In particular, we will show that even though the unique positive constant steady-state is stable for the ODE dynamics, non-constant positive steady-states exist for the reaction diffusion system. This demonstrates that stationary patterns arise as a result of diffusion.