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Zbl 1152.34046
Ding, Xiaohua; Lu, Chun; Liu, Mingzhu
Periodic solutions for a semi-ratio-dependent predator-prey system with nonmonotonic functional response and time delay. (English)
[J] Nonlinear Anal., Real World Appl. 9, No. 3, 762-775 (2008). ISSN 1468-1218

By using the continuation theorem of coincidence degree theory, the existence of a positive periodic solution for a semi-ratio-dependent predator-prey system with nonmonotonic functional responses and time delay is established. Further, by constructing a Lyapunov functional, a set of easily verifiable sufficient conditions are derived for the uniqueness and global stability of positive periodic solutions to the system. Finally, some numerical simulations are carried out to illustrate the effectiveness of the new results.
[Xinyu Song (Xinyang)]

MSC 2000:: *34K13 Periodic solutions of functional differential equations
34K20 Stability theory of functional-differential equations
92D25 Population dynamics

Keywords: nonmonotonic functional response; semi-ratio-dependent; predator-prey system; time delay; periodic solution; Lyapunov functional; global stability

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