On the Uniqueness and Dependence of Positive Periodic Solutions for Delay Differential Systems with Feedback Control
This paper investigates a class of delay differential systems with feedback control. Sufficient conditions are obtained for the existence and uniqueness of the positive periodic solution by utilizing some results from the mixed monotone operator theory. Meanwhile, the dependence of the positive peri...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2012-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2012/971427 |
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| _version_ | 1850109584408051712 |
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| author | Haitao Li Yansheng Liu |
| author_facet | Haitao Li Yansheng Liu |
| author_sort | Haitao Li |
| collection | DOAJ |
| description | This paper investigates a class of delay differential systems with feedback control. Sufficient conditions are obtained for the existence and uniqueness of the positive periodic solution by utilizing some results from the mixed monotone operator theory. Meanwhile, the dependence of the positive periodic solution on the parameter λ is also studied. Finally, an example together with numerical simulations is worked out to illustrate the main results. |
| format | Article |
| id | doaj-art-4889f90ca23443fab2acfa8829b6ab46 |
| institution | OA Journals |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-4889f90ca23443fab2acfa8829b6ab462025-08-20T02:38:02ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252012-01-01201210.1155/2012/971427971427On the Uniqueness and Dependence of Positive Periodic Solutions for Delay Differential Systems with Feedback ControlHaitao Li0Yansheng Liu1School of Control Science and Engineering, Shandong University, Jinan 250061, ChinaDepartment of Mathematics, Shandong Normal University, Jinan 250014, ChinaThis paper investigates a class of delay differential systems with feedback control. Sufficient conditions are obtained for the existence and uniqueness of the positive periodic solution by utilizing some results from the mixed monotone operator theory. Meanwhile, the dependence of the positive periodic solution on the parameter λ is also studied. Finally, an example together with numerical simulations is worked out to illustrate the main results.http://dx.doi.org/10.1155/2012/971427 |
| spellingShingle | Haitao Li Yansheng Liu On the Uniqueness and Dependence of Positive Periodic Solutions for Delay Differential Systems with Feedback Control International Journal of Mathematics and Mathematical Sciences |
| title | On the Uniqueness and Dependence of Positive Periodic Solutions for Delay Differential Systems with Feedback Control |
| title_full | On the Uniqueness and Dependence of Positive Periodic Solutions for Delay Differential Systems with Feedback Control |
| title_fullStr | On the Uniqueness and Dependence of Positive Periodic Solutions for Delay Differential Systems with Feedback Control |
| title_full_unstemmed | On the Uniqueness and Dependence of Positive Periodic Solutions for Delay Differential Systems with Feedback Control |
| title_short | On the Uniqueness and Dependence of Positive Periodic Solutions for Delay Differential Systems with Feedback Control |
| title_sort | on the uniqueness and dependence of positive periodic solutions for delay differential systems with feedback control |
| url | http://dx.doi.org/10.1155/2012/971427 |
| work_keys_str_mv | AT haitaoli ontheuniquenessanddependenceofpositiveperiodicsolutionsfordelaydifferentialsystemswithfeedbackcontrol AT yanshengliu ontheuniquenessanddependenceofpositiveperiodicsolutionsfordelaydifferentialsystemswithfeedbackcontrol |