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Positive periodic solutions of a class of non-autonomous single species population models with delays and feedback control. (English) Zbl 1110.34049

The authors consider a class of nonautonomous single species population models with delays and feedback control. By using the continuation theorem of coincidence degree, several verifiable conditions are given to establish the global existence of positive periodic solutions. Moreover, the existence of a unique globally asymptotic stable positive periodic solution of a kind of nonlinear feedback control ecosystem is obtained by constructing a Lyapunov function. To illustrate the theory, a multiplicative state-dependent delay periodic Logistic equation with feedback control is considered.

MSC:

34K13 Periodic solutions to functional-differential equations
92D25 Population dynamics (general)
34D20 Stability of solutions to ordinary differential equations
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