Global stability and periodic orbits for a two-patch diffusion predator-prey model with time delays (Q1585035)

Here, a predator-prey model, involving continuous time-delays and diffusion, is considered. The boundedness of solutions to this model is established with the help of comparison theorems of differential equations. The existence of a nonzero globally stable equilibrium is proved using Lyapunov functions. The existence of a periodic orbit of Hopf type from the equilibrium is shown by means of the theory of Hopf bifurcation. Some ecological implications of the main results are discussed. The authors analyzed the possible effects of both the diffusion and the time-delay on the stability of the model.