Abstract: In this paper, a Lotka-Volterra type predator-prey model with time delays due to gestation of the predator and dispersal for both the prey and the predator is investigated. We first establish two different results on the permanence of the system. Using coincidence degree theory, sufficient conditions are derived for the existence of positive periodic solutions, and by constructing an appropriate Lyapunov functional, we further discuss their uniqueness and global stability. Numerical simulations are carried out to illustrate the main results.

Key words: delay, dispersal, periodic solution, global stability