Hopf Bifurcation Analysis in a New Chaotic System with Chaos Entanglement Function
A new approach to generate chaotic phenomenon, called chaos entanglement, is introduced in this paper. The basic principle is to entangle two or multiple stable linear subsystems by entanglement functions to form an artificial chaotic system such that each of them evolves in a chaotic manner. The Ho...
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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/10.1155/2014/371509 |
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| _version_ | 1832554388923613184 |
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| author | Zhang Jiangang Chu Yandong Du Wenju Chang Yingxiang An Xinlei |
| author_facet | Zhang Jiangang Chu Yandong Du Wenju Chang Yingxiang An Xinlei |
| author_sort | Zhang Jiangang |
| collection | DOAJ |
| description | A new approach to generate chaotic phenomenon, called chaos entanglement, is introduced in this paper. The basic principle is to entangle two or multiple stable linear subsystems by entanglement functions to form an artificial chaotic system such that each of them evolves in a chaotic manner. The Hopf bifurcation of a new chaotic system with chaos entanglement function is studied. More precisely, we study the stability and bifurcations of equilibrium in the new chaotic system. Besides, we controlled the system to any fixed point 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-d4386e9846444b4bb4c67934b36c0e79 |
| 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-d4386e9846444b4bb4c67934b36c0e792025-02-03T05:51:40ZengWileyJournal of Applied Mathematics1110-757X1687-00422014-01-01201410.1155/2014/371509371509Hopf Bifurcation Analysis in a New Chaotic System with Chaos Entanglement FunctionZhang Jiangang0Chu Yandong1Du Wenju2Chang Yingxiang3An Xinlei4Department of Mathematics, Lanzhou Jiaotong University, Lanzhou 730070, ChinaDepartment of Mathematics, Lanzhou Jiaotong University, Lanzhou 730070, ChinaDepartment of Mathematics, Lanzhou Jiaotong University, Lanzhou 730070, ChinaDepartment of Mathematics, Lanzhou Jiaotong University, Lanzhou 730070, ChinaDepartment of Mathematics, Lanzhou Jiaotong University, Lanzhou 730070, ChinaA new approach to generate chaotic phenomenon, called chaos entanglement, is introduced in this paper. The basic principle is to entangle two or multiple stable linear subsystems by entanglement functions to form an artificial chaotic system such that each of them evolves in a chaotic manner. The Hopf bifurcation of a new chaotic system with chaos entanglement function is studied. More precisely, we study the stability and bifurcations of equilibrium in the new chaotic system. Besides, we controlled the system to any fixed point 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/10.1155/2014/371509 |
| spellingShingle | Zhang Jiangang Chu Yandong Du Wenju Chang Yingxiang An Xinlei Hopf Bifurcation Analysis in a New Chaotic System with Chaos Entanglement Function Journal of Applied Mathematics |
| title | Hopf Bifurcation Analysis in a New Chaotic System with Chaos Entanglement Function |
| title_full | Hopf Bifurcation Analysis in a New Chaotic System with Chaos Entanglement Function |
| title_fullStr | Hopf Bifurcation Analysis in a New Chaotic System with Chaos Entanglement Function |
| title_full_unstemmed | Hopf Bifurcation Analysis in a New Chaotic System with Chaos Entanglement Function |
| title_short | Hopf Bifurcation Analysis in a New Chaotic System with Chaos Entanglement Function |
| title_sort | hopf bifurcation analysis in a new chaotic system with chaos entanglement function |
| url | http://dx.doi.org/10.1155/2014/371509 |
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