| 一种复非线性系统的动力学特性和同步分析 |
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| 引用本文： | 琚宏昌,李红远. 一种复非线性系统的动力学特性和同步分析[J]. 控制理论与应用, 2012, 29(9): 1181-1185 |
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| 作者姓名： | 琚宏昌 李红远 |
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| 作者单位： | 广西工学院鹿山学院土木工程系,广西柳州,545616 |
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| 基金项目： | 广西教育厅自然科学基金资助项目(200911MS115, 201010LX215). |
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| 摘 要： | 本文介绍一种新复非线性系统并研究它的动力学特性(包括不变量、耗散度、平衡和稳定性、Lyapunov指数、混沌行为、混沌吸引子),以及该系统产生混沌的必要条件,发现在一定参数条件下,系统存在2个或4个螺线形混沌吸引子,通过研究驱动系统和响应系统的关系,导出了混沌同步的控制函数显式表达式.Lyapunov函数分析证明,系统误差是渐近稳定的,控制函数可以使主动系统和响应系统完全同步.
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| 关 键 词： | 混沌 吸引子 同步 主动控制 平衡和稳定性 |
| 收稿时间： | 2011-07-10 |
| 修稿时间： | 2012-01-07 |
Dynamical properties and synchronization analysis for a complex nonlinear systems |
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| QU Hong-chang and LI Hong-yuan. Dynamical properties and synchronization analysis for a complex nonlinear systems[J]. Control Theory & Applications, 2012, 29(9): 1181-1185 |
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| Authors: | QU Hong-chang and LI Hong-yuan |
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| Affiliation: | Department of Civil Engineering, Lushan College of Guangxi University of Technology,Department of Civil Engineering, Lushan College of Guangxi University of Technology |
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| Abstract: | This paper introduces a new complex nonlinear system and studies their dynamic properties including the invariance, dissipativity, equilibria of stability, Lyapunov exponents, chaotic behaviors, chaotic attractors, along with necessary conditions for this system to generate a chaos. It is found that there are 2 or 4-scroll chaotic attractors for certain values of system parameters. Chaos synchronization of these attractors is studied via the active control, and explicit expressions for control functions to achieve chaos synchronization are derived. By using Lyapunov function, we prove that the error system is asymptotically stable, and the control function can completely synchronize both the active system and the response system. |
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| Keywords: | chaos attractor synchronization active control equilibria of stability |
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