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Dynamic of a non-autonomous predator-prey system with infinite delay and diffusion. (English) Zbl 1155.34329
Summary: 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.
34D05Asymptotic stability of ODE
34D23Global stability of ODE
92D25Population dynamics (general)
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