Dynamic of a non-autonomous predator–prey system with infinite delay and diffusion

In the present paper, a nonlinear non-autonomous predator–prey dispersion model with continuous delay is studied. Sufficient conditions which guarantee the existence of a periodic positive solution are obtained by using Gaines and Mawhin’s continuation theorem of coincidence degree theory. Moreover, globally asymptotically stability of the system is also obtained by means of a suitable Lyapunov functional. The applications show that these criteria are easily verified.