This talk concerns with a reaction-diffusion system modeling the population dynamics of
two predators and one prey with nonlinear prey-taxis. We first investigate the global existence
and boundedness of solution for the general model. Then we study the global stabilities of
nonnegative spatially homogeneous equilibria for an explicit system with type I functional
responses and density-dependent death rates for the predators and logistic growth for the
prey. Moreover, the convergence rates are established.