Positive Periodic Solutions of a Class of Nonautonomous Single Species Population Model with Delays and Feedback Control

With the help of a continuation theorem based on Gaines and Mawhin's coincidence degree, several verifiable criteria are established for the global existence of positive periodic solutions of a class of non.autonomous single species population model with delays (both state.dependent delays and continuous delays) and feedback control. After that, by constructing a suitable Lyapunov functional, sufficient conditions which guarantee the existence of a unique globally asymptotic stable positive periodic solution of a kind of nonlinear feedback control ecosystem are obtained. Our results extend and improve the existing results, and have further applications in population dynamics.