Analysis on the existence of the steady-states for an ecological-mathematical model with predator-prey-dependent functional response

We establish a reaction-diffusion ecological-mathematical model with predator-prey dependent functional response and the Neumann boundary conditions. First, we study the bifurcation solution emitting from the unique positive constant solution by considering the local bifurcation. Finally, we mainly analyze the coexistence of the prey and predator with the help of the fixed point index theory, where we use a different approach in calculating one of the fixed point indices.