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-autonomou...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.展开更多
基金supported by the National Natural Science Foundation of China under the Grant(10426010)the Foundation of Science and Technology of Fujian Province for Young Scholars(2004J0002)+3 种基金the Foundation of Fujian Education Bureau(JA04156)the National Natural Science Foundation of China under Grant 60373067the Natural Science Foundation of Jiangsu Province,China under Grants BK2003053Qing-Lan Engineering Project of Jiangsu Province,the Foundation of Southeast University,Nanjing,China under Grant XJ030714
文摘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.
