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Permanence and global attractivity of a discrete semi-ratio dependent predator-prey system with Holling II type functional response. (English) Zbl 1213.49046

Summary: We propose a discrete semi-ratio dependent predator-prey system with Holling II type functional response. For general nonautonomous case, sufficient conditions which ensure the permanence and the global stability of the system are obtained; for periodic case, sufficient conditions which ensure the existence of a globally stable positive periodic solution of the system are obtained.

MSC:

49N75 Pursuit and evasion games
49M25 Discrete approximations in optimal control
34C25 Periodic solutions to ordinary differential equations
34D23 Global stability of solutions to ordinary differential equations
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