| Positive Periodic Solutions of a Class of Non-autonomous Single Species Population Model with Delays and Feedback Control |
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| 作者姓名： | Feng De CHEN Xiao Xin CHEN Jin De CAO An Ping CHEN |
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| 作者单位： | [1]College of Mathematics and Computer Science, Fuzhou University, Fuzhou 350002, P. R. China [2]Department of Mathematics, Southeast University, Nanjing 210096, P, R. China [3]Department of Mathematics, Xiangnan College, Chenzhou 423000, P. R. China |
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| 摘 要： | 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.
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| 关 键 词： | 正周期解 时滞系统 一致度 延拓理论 存在性 |
| 收稿时间： | 2003-08-18 |
| 修稿时间： | 2003-08-182004-09-02 |
Positive Periodic Solutions of a Class of Non–autonomous Single Species Population Model with Delays and Feedback Control |
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| Feng De CHEN Xiao Xin CHEN Jin De CAO An Ping CHEN.Positive Periodic Solutions of a Class of Non-autonomous Single Species Population Model with Delays and Feedback Control[J].Acta Mathematica Sinica,2005,21(6):1319-1336. |
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| Authors: | Feng De Chen Xiao Xin Chen Jin De Cao An Ping Chen |
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| Institution: | (1) College of Mathematics and Computer Science, Fuzhou University, Fuzhou 350002, P. R. China;(2) Department of Mathematics, Southeast University, Nanjing 210096, P. R. China;(3) Department of Mathematics, Xiangnan College, Chenzhou 423000, P. R. China |
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| Abstract: | 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.
This work was 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), the Foundation of Fujian Education Bureau (JA04156),
the National Natural Science Foundation of China under Grant 60373067, the Natural Science Foundation of Jiangsu Province,
China under Grants BK2003053, Qing-Lan Engineering Project of Jiangsu Province, the Foundation of Southeast University, Nanjing,
China under Grant XJ030714 |
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| Keywords: | Positive periodic solutions Delays Coincidence degree Single species model |
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