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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.

Reviewer: Hai-Feng Huo (Lanzhou)

### MSC:

34K13 | Periodic solutions to functional-differential equations |

92D25 | Population dynamics (general) |

34D20 | Stability of solutions to ordinary differential equations |

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\textit{F. De Chen} et al., Acta Math. Sin., Engl. Ser. 21, No. 6, 1319--1336 (2005; Zbl 1110.34049)

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### References:

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