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Periodic solutions of delayed Leslie-Gower predator-prey models. (English) Zbl 1060.34039

Authors’ abstract: With the help of continuation theorem based on Gaines and Mawhin’s conincidence degree, sufficient and realistic conditions are obtained for the global existence of positive periodic solutions for both the first and the second Leslie-Gower predator-prey models with distributed or state dependent delay.

In the reviewer’s opinion, a relevant reference is [Q. Liu and H. Zhou, JIPAM, J. Inequal. Pure Appl. Math. 4, No. 5, Paper No. 89 (2003; Zbl 1069.34063)] where coincidence degree is used to prove existence and global attractivity of periodic solutions in an n-species food chain system with time delays.

34K13Periodic solutions of functional differential equations
92D25Population dynamics (general)