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Existence and global stability of periodic solutions of a discrete predator-prey system with delays. (English) Zbl 1043.92038

Summary: With the help of the continuation theorem in coincidence degree theory and Lyapunov functions, we derive sufficient and realistic conditions that guarantee the existence of positive periodic solutions for a delayed discrete predator-prey system, and also obtain sufficient conditions for the global stability of positive periodic solutions.

MSC:

92D40 Ecology
39A12 Discrete version of topics in analysis
37N25 Dynamical systems in biology
39A11 Stability of difference equations (MSC2000)
34K13 Periodic solutions to functional-differential equations
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