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Uniform persistence and periodic solutions for a discrete predator-prey system with delays. (English) Zbl 1107.39017
This paper deals with a class of discrete predator-prey systems with delay. A sufficient condition for the uniform persistence of the system is first shown, and then, if the coefficients in the system are periodic, the existence of a periodic solution based on the uniform persistence result is obtained by generalizing the Yoshizawa’s theorem on the existence of periodic solution for ordinary differential equation to the difference equations with delays.

MSC:
39A11 Stability of difference equations (MSC2000)
39A12 Discrete version of topics in analysis
34K13 Periodic solutions to functional-differential equations
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