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Periodic solutions of a nonautonomous predator–prey system with stage structure and time delays. (English) Zbl 1110.34051
Abstract: “A nonautonomous Lotka-Volterra-type predator-prey model with stage structure and time delays is investigated. It is assumed in the model that the individuals in each species may belong to one of two classes: the immatures and the matures, the age to maturity is presented by a time delay, and that the immature predators do not feed on prey and do not have the ability to produce. By some comparison arguments, we first discuss the permanence of the model. By using the continuation theorem of coincidence degree theory, sufficient conditions are derived for the existence of positive periodic solutions to the model. By means of a suitable Lyapunov functional, sufficient conditions are obtained for the uniqueness and global stability of the positive periodic solutions to the model.”
34K13Periodic solutions of functional differential equations
34K60Qualitative investigation and simulation of models
92D25Population dynamics (general)