| 一类三次方对称离散混沌系统的分岔控制 |
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| 引用本文： | 张惠,褚衍东,丁旺才,李险峰.一类三次方对称离散混沌系统的分岔控制[J].物理学报,2013,62(4):40202-040202. |
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| 作者姓名： | 张惠 褚衍东 丁旺才 李险峰 |
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| 作者单位： | 1. 兰州交通大学机电工程学院, 兰州 730070;2. 兰州交通大学数学系, 兰州 730070;3. 香港城市大学土木与建筑工程系, 香港 |
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| 基金项目： | 国家自然科学基金(批准号:11161027,11162007)、甘肃省自然科学重点基金(批准号:1010RJZA067)和兰州交通大学青年科学基金(批准号:2011026)资助的课题. |
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| 摘 要： | 通过分析对称性破缺分岔机制, 采用了一个直接的、有效的线性控制器, 精确控制了一类三次方对称离散混沌系统发生对称性破缺分岔和倍周期分岔时分岔点的位置. 进而分析了系统对初始值的敏感性和对称性, 选择合适的吸引域, 将对称性破缺分岔进行进一步控制, 从而使得对称性破缺分岔所缺解枝得以恢复. 数值结果表明了该控制器的有效性.
关键词：
离散混沌系统
对称性破缺
倍周期
分岔控制
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| 关 键 词： | 离散混沌系统 对称性破缺 倍周期 分岔控制 |
| 收稿时间： | 2012-08-05 |
Bifurcation control of a cubic symmetry discrete chaotic system |
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| Zhang Hui,Chu Yan-Dong,Ding Wang-Cai,Li Xian-Feng.Bifurcation control of a cubic symmetry discrete chaotic system[J].Acta Physica Sinica,2013,62(4):40202-040202. |
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| Authors: | Zhang Hui Chu Yan-Dong Ding Wang-Cai Li Xian-Feng |
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| Institution: | 1. School of Mechatronic Engineering, Lanzhou Jiaotong University, Lanzhou 730070, China;2. Department of Mathematics, Lanzhou Jiaotong University, Lanzhou 730070, China;3. Department of Civil and Architectural Engineering, City University of Hong Kong, Hong Kong |
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| Abstract: | A direct and effective linear-controller is employed to exactly control the locations of bifurcation points, both the symmetry-breaking bifurcation and the period-doubling bifurcation, in a cubic symmetry discrete system. Moreover, both the sensibility and the symmetry to the initial values of the system are analyzed. The lack of the solution branches due to the symmetry-breaking bifurcation can be reinstated temporarily by selecting the corresponding basins of attraction. The effectiveness of the controller is verified by numerical simulations. |
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| Keywords: | discrete chaotic system symmetry-breaking period-doubling bifurcation control |
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