Bifurcation Analysis and Sliding Mode Control of Chaotic Vibrations in an Autonomous System
We study the bifurcations and sliding mode control of chaotic vibrations in an autonomous system. More precisely, a Hopf bifurcation controller is designed so as to control the unstable subcritical Hopf bifurcation to the stable supercritical Hopf bifurcation. Research result shows that the control...
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| Main Authors: | , , , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2014/726491 |
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| _version_ | 1832556366115373056 |
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| author | Wenju Du Yandong Chu Jiangang Zhang Yingxiang Chang Jianning Yu Xinlei An |
| author_facet | Wenju Du Yandong Chu Jiangang Zhang Yingxiang Chang Jianning Yu Xinlei An |
| author_sort | Wenju Du |
| collection | DOAJ |
| description | We study the bifurcations and sliding mode control of chaotic vibrations in an autonomous system. More precisely, a Hopf bifurcation controller is designed so as to control the unstable subcritical Hopf bifurcation to the stable supercritical Hopf bifurcation. Research result shows that the control method can work very well in Hopf bifurcation control. Besides, we controlled the system to any fixed point and any periodic orbit to eliminate the chaotic vibration by means of sliding mode method. And the numerical simulations were presented to confirm the effectiveness of the controller. |
| format | Article |
| id | doaj-art-d654a08932424b8caee25d4eff230391 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-d654a08932424b8caee25d4eff2303912025-02-03T05:45:38ZengWileyJournal of Applied Mathematics1110-757X1687-00422014-01-01201410.1155/2014/726491726491Bifurcation Analysis and Sliding Mode Control of Chaotic Vibrations in an Autonomous SystemWenju Du0Yandong Chu1Jiangang Zhang2Yingxiang Chang3Jianning Yu4Xinlei An5Department of Mathematics, Lanzhou Jiaotong University, Lanzhou, Gansu 730070, ChinaDepartment of Mathematics, Lanzhou Jiaotong University, Lanzhou, Gansu 730070, ChinaDepartment of Mathematics, Lanzhou Jiaotong University, Lanzhou, Gansu 730070, ChinaDepartment of Mathematics, Lanzhou Jiaotong University, Lanzhou, Gansu 730070, ChinaDepartment of Mathematics, Lanzhou Jiaotong University, Lanzhou, Gansu 730070, ChinaDepartment of Mathematics, Lanzhou Jiaotong University, Lanzhou, Gansu 730070, ChinaWe study the bifurcations and sliding mode control of chaotic vibrations in an autonomous system. More precisely, a Hopf bifurcation controller is designed so as to control the unstable subcritical Hopf bifurcation to the stable supercritical Hopf bifurcation. Research result shows that the control method can work very well in Hopf bifurcation control. Besides, we controlled the system to any fixed point and any periodic orbit to eliminate the chaotic vibration by means of sliding mode method. And the numerical simulations were presented to confirm the effectiveness of the controller.http://dx.doi.org/10.1155/2014/726491 |
| spellingShingle | Wenju Du Yandong Chu Jiangang Zhang Yingxiang Chang Jianning Yu Xinlei An Bifurcation Analysis and Sliding Mode Control of Chaotic Vibrations in an Autonomous System Journal of Applied Mathematics |
| title | Bifurcation Analysis and Sliding Mode Control of Chaotic Vibrations in an Autonomous System |
| title_full | Bifurcation Analysis and Sliding Mode Control of Chaotic Vibrations in an Autonomous System |
| title_fullStr | Bifurcation Analysis and Sliding Mode Control of Chaotic Vibrations in an Autonomous System |
| title_full_unstemmed | Bifurcation Analysis and Sliding Mode Control of Chaotic Vibrations in an Autonomous System |
| title_short | Bifurcation Analysis and Sliding Mode Control of Chaotic Vibrations in an Autonomous System |
| title_sort | bifurcation analysis and sliding mode control of chaotic vibrations in an autonomous system |
| url | http://dx.doi.org/10.1155/2014/726491 |
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