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Periodicity and asymptotic stability of a predator-prey system with infinite delays. (English) Zbl 1201.34111
Summary: By using a fixed point theorem and Lyapunov functional, an especially easily checked criterion is obtained for the global existence and global asymptotic stability of positive periodic solutions of a periodic predator-prey system with infinite delays. Moreover, the global existence theorem is also sufficient and necessary. This result improves and generalizes noticeably some known results.
MSC:
34K13Periodic solutions of functional differential equations
92D25Population dynamics (general)
34K20Stability theory of functional-differential equations
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