Spatiotemporal dynamics of a predator-prey system with prey-taxis and intraguild predation

This paper is concerned with a reaction-diffusion predator-prey model with prey-taxis and intraguild predation. We first discuss the basic properties of solutions with the aid of differential equation theory. Then, we investigate the local and global stability of constant equilibrium solution by linear stability analysis and Lyapunov function method, respectively. Moreover, we establish the existences of nonconstant positive steady states and time-periodic solutions through detailed bifurcation analyses. Finally, we give some numerical simulations and conclusions to illustrate the theoretical findings.