Control of Hopf Bifurcation and Chaos in a Delayed Lotka-Volterra Predator-Prey System with Time-Delayed Feedbacks
A delayed Lotka-Volterra predator-prey system with time delayed feedback is studied by using the theory of functional differential equation and Hassard’s method. By choosing appropriate control parameter, we investigate the existence of Hopf bifurcation. An explicit algorithm is given to determine t...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/104156 |
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| _version_ | 1832564644212899840 |
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| author | Huitao Zhao Yaowei Sun Zhen Wang |
| author_facet | Huitao Zhao Yaowei Sun Zhen Wang |
| author_sort | Huitao Zhao |
| collection | DOAJ |
| description | A delayed Lotka-Volterra predator-prey system with time delayed feedback is studied by using the theory of functional differential equation and Hassard’s method. By choosing appropriate control parameter, we investigate the existence of Hopf bifurcation. An explicit algorithm is given to determine the directions and stabilities of the bifurcating periodic solutions. We find that these control laws can be applied to control Hopf bifurcation and chaotic attractor. Finally, some numerical simulations are given to illustrate the effectiveness of the results found. |
| format | Article |
| id | doaj-art-e56c4bd3b61d48c6bb962de61370d007 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-e56c4bd3b61d48c6bb962de61370d0072025-02-03T01:10:32ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/104156104156Control of Hopf Bifurcation and Chaos in a Delayed Lotka-Volterra Predator-Prey System with Time-Delayed FeedbacksHuitao Zhao0Yaowei Sun1Zhen Wang2Department of Mathematics and Information Science, Zhoukou Normal University, Zhoukou, Henan 466001, ChinaDepartment of Mathematics and Information Science, Zhoukou Normal University, Zhoukou, Henan 466001, ChinaInstitute of Information and System Computation Science, Beifang University of Nationalities, Yinchuan, Ningxia 750021, ChinaA delayed Lotka-Volterra predator-prey system with time delayed feedback is studied by using the theory of functional differential equation and Hassard’s method. By choosing appropriate control parameter, we investigate the existence of Hopf bifurcation. An explicit algorithm is given to determine the directions and stabilities of the bifurcating periodic solutions. We find that these control laws can be applied to control Hopf bifurcation and chaotic attractor. Finally, some numerical simulations are given to illustrate the effectiveness of the results found.http://dx.doi.org/10.1155/2014/104156 |
| spellingShingle | Huitao Zhao Yaowei Sun Zhen Wang Control of Hopf Bifurcation and Chaos in a Delayed Lotka-Volterra Predator-Prey System with Time-Delayed Feedbacks Abstract and Applied Analysis |
| title | Control of Hopf Bifurcation and Chaos in a Delayed Lotka-Volterra Predator-Prey System with Time-Delayed Feedbacks |
| title_full | Control of Hopf Bifurcation and Chaos in a Delayed Lotka-Volterra Predator-Prey System with Time-Delayed Feedbacks |
| title_fullStr | Control of Hopf Bifurcation and Chaos in a Delayed Lotka-Volterra Predator-Prey System with Time-Delayed Feedbacks |
| title_full_unstemmed | Control of Hopf Bifurcation and Chaos in a Delayed Lotka-Volterra Predator-Prey System with Time-Delayed Feedbacks |
| title_short | Control of Hopf Bifurcation and Chaos in a Delayed Lotka-Volterra Predator-Prey System with Time-Delayed Feedbacks |
| title_sort | control of hopf bifurcation and chaos in a delayed lotka volterra predator prey system with time delayed feedbacks |
| url | http://dx.doi.org/10.1155/2014/104156 |
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