In this paper, we consider a diffusive Lotka-Volterra predator-prey system with spatial heterogeneity and two delays. We first show that there exists a nonconstant positive steady state when the diffusion rates of prey and predator are large. Then we obtain the stability of the steady state and show the existence of a Hopf bifurcation. Moreover, some numerical simulations are provided to illustrate our theoretical results.
MSC 2010: 35K57, 37G15, 37N25, 92D25