| The generation of a hyperchaotic system based on a three-dimensional autonomous chaotic system |
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| 作者姓名： | 王杰智 陈增强 袁著祉 |
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| 作者单位： | Department of Automation, Nankai University,Tianjin 300070, China;Department of Automation, Nankai University,Tianjin 300070, China;Department of Automation, Nankai University,Tianjin 300070, China |
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| 基金项目： | Project supported by the National Natural Science Foundation of China (Grant Nos 60374037 and 60574036), the Specialized Research Fund for the Doctoral Program of China (Grant No
20050055013) and the Program for New Century Excellent Talents in University of China (NCET). |
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| 摘 要： | This paper reports a new four-dimensional hyperchaotic system obtained by adding a controller to a threedimensional autonomous chaotic system. The new system has two parameters, and each equation of the system has one quadratic cross-product term. Some basic properties of the new system are analysed. The different dynamic behaviours of the new system are studied when the system parameter a or b is varied. The system is hyperchaotic in several different regions of the parameter b. Especially, the two positive Lyapunov exponents are both larger, and the hyperchaotic region is also larger when this system is hyperchaotic in the case of varying a. The hyperchaotic system is analysed by Lyapunov-exponents spectrum, bifurcation diagrams and Poincaré sections.
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| 关 键 词： | 混沌性 不规则代 超混乱系统 二分叉分析 |
| 收稿时间： | 2006-01-16 |
| 修稿时间： | 2006-01-162006-02-23 |
The generation of a hyperchaotic system based on a three-dimensional autonomous chaotic system |
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| Wang Jie-Zhi,Chen Zeng-Qiang and Yuan Zhu-Zhi.The generation of a hyperchaotic system based on a three-dimensional autonomous chaotic system[J].Chinese Physics B,2006,15(6):1216-1225. |
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| Authors: | Wang Jie-Zhi Chen Zeng-Qiang and Yuan Zhu-Zhi |
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| Institution: | Department of Automation, Nankai University,Tianjin 300070, China |
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| Abstract: | This paper reports a new four-dimensional hyperchaotic system obtained by
adding a controller to a three-dimensional autonomous chaotic system. The
new system has two parameters, and each equation of the system has one
quadratic cross-product term. Some basic properties of the new system are
analysed. The different dynamic behaviours of the new system are studied when
the system parameter $a$ or $b$ is varied. The system is hyperchaotic in
several different regions of the parameter $b$. Especially, the two positive
Lyapunov exponents are both larger, and the hyperchaotic region is also
larger when this system is hyperchaotic in the case of varying $a$. The
hyperchaotic system is analysed by Lyapunov-exponents spectrum, bifurcation
diagrams and Poincar\'{e} sections. |
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| Keywords: | chaos chaos generation hyperchaotic system bifurcation analysis |
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