Hopf Bifurcation Control in a Delayed Predator-Prey System with Prey Infection and Modified Leslie-Gower Scheme
Hopf bifurcation of a delayed predator-prey system with prey infection and the modified Leslie-Gower scheme is investigated. The conditions for the stability and existence of Hopf bifurcation of the system are obtained. The state feedback and parameter perturbation are used for controlling Hopf bifu...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/704320 |
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| _version_ | 1849411045314002944 |
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| author | Zizhen Zhang Huizhong Yang |
| author_facet | Zizhen Zhang Huizhong Yang |
| author_sort | Zizhen Zhang |
| collection | DOAJ |
| description | Hopf bifurcation of a delayed predator-prey system with prey infection and the modified Leslie-Gower scheme is investigated. The conditions for the stability and existence of Hopf bifurcation of the system are obtained. The state feedback and parameter perturbation are used for controlling Hopf bifurcation in the system. In addition, direction of Hopf bifurcation and stability of the bifurcated periodic solutions of the controlled system are obtained by using normal form and center manifold theory. Finally, numerical simulation results are presented to show that the hybrid controller is efficient in controlling Hopf bifurcation. |
| format | Article |
| id | doaj-art-5c716830cf744bd9baadf68c248df23f |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-5c716830cf744bd9baadf68c248df23f2025-08-20T03:34:53ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/704320704320Hopf Bifurcation Control in a Delayed Predator-Prey System with Prey Infection and Modified Leslie-Gower SchemeZizhen Zhang0Huizhong Yang1Key Laboratory of Advanced Process Control for Light Industry of the Ministry of Education, Jiangnan University, Wuxi 214122, ChinaKey Laboratory of Advanced Process Control for Light Industry of the Ministry of Education, Jiangnan University, Wuxi 214122, ChinaHopf bifurcation of a delayed predator-prey system with prey infection and the modified Leslie-Gower scheme is investigated. The conditions for the stability and existence of Hopf bifurcation of the system are obtained. The state feedback and parameter perturbation are used for controlling Hopf bifurcation in the system. In addition, direction of Hopf bifurcation and stability of the bifurcated periodic solutions of the controlled system are obtained by using normal form and center manifold theory. Finally, numerical simulation results are presented to show that the hybrid controller is efficient in controlling Hopf bifurcation.http://dx.doi.org/10.1155/2013/704320 |
| spellingShingle | Zizhen Zhang Huizhong Yang Hopf Bifurcation Control in a Delayed Predator-Prey System with Prey Infection and Modified Leslie-Gower Scheme Abstract and Applied Analysis |
| title | Hopf Bifurcation Control in a Delayed Predator-Prey System with Prey Infection and Modified Leslie-Gower Scheme |
| title_full | Hopf Bifurcation Control in a Delayed Predator-Prey System with Prey Infection and Modified Leslie-Gower Scheme |
| title_fullStr | Hopf Bifurcation Control in a Delayed Predator-Prey System with Prey Infection and Modified Leslie-Gower Scheme |
| title_full_unstemmed | Hopf Bifurcation Control in a Delayed Predator-Prey System with Prey Infection and Modified Leslie-Gower Scheme |
| title_short | Hopf Bifurcation Control in a Delayed Predator-Prey System with Prey Infection and Modified Leslie-Gower Scheme |
| title_sort | hopf bifurcation control in a delayed predator prey system with prey infection and modified leslie gower scheme |
| url | http://dx.doi.org/10.1155/2013/704320 |
| work_keys_str_mv | AT zizhenzhang hopfbifurcationcontrolinadelayedpredatorpreysystemwithpreyinfectionandmodifiedlesliegowerscheme AT huizhongyang hopfbifurcationcontrolinadelayedpredatorpreysystemwithpreyinfectionandmodifiedlesliegowerscheme |