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Periodic solutions for a predator-prey model with Holling-type functional response and time delays. (English) Zbl 1064.34053

Authors’ abstract: A delayed periodic predator-prey model with Holling-type functional response and time delays is investigated. Using Gaines-Mawhin coincidence degree theorem and by constructing a suitable Lyapunov functional, a set of sufficient conditions are derived for the existence, uniqueness and global stability of a positive periodic solution to the model. Numerical simulation is carried out to illustrate the feasibility of our main results.

The reviewer likes to add the following relevant references: H. Huo and W. Li [Appl. Math. Comput. 155, 591–605 (2004; Zbl 1060.34049) and ibid. 156, 871–882 (2004; Zbl 1064.34046).

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