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山东大学学报（理学版） ›› 2015, Vol. 50 ›› Issue (11): 104-112.doi: 10.6040/j.issn.1671-9352.0.2014.443

• 论文 • 上一篇    下一篇

一个新四维光滑四翼超混沌系统及电路实现

王杰智1, 李航2, 王蕊3, 王鲁4, 王晏超5   

  1. 1. 中国民航大学理学院, 天津 300300;
    2. 中国民航大学经济与管理学院, 天津 300300;
    3. 中国民航大学航空自动化学院航空电气系, 天津 300300;
    4. 山东国强五金科技有限公司总工办, 山东 乐陵 253600;
    5. 中国东方航空股份有限公司工程技术公司维修管理部, 上海 200335
  • 收稿日期:2014-10-09 修回日期:2015-02-11 出版日期:2015-11-20 发布日期:2015-12-09
  • 作者简介:王杰智(1978-),女,博士,讲师,研究方向为混沌分析和反控制研究.E-mail:wjzh197845@163.com
  • 基金资助:
    国家自然科学基金资助项目(11472298,11102226);中央高校基本科研业务费专项资金资助项目(ZXH2010D011,ZXH2012B003,ZXH2012K002);中国民航大学科研启动基金资助项目(07QD05X)

A new four-dimensional smooth four-wing hyperchaotic system and its circuit implementation

WANG Jie-zhi1, LI Hang2, WANG Rui3, WANG Lu4, WANG Yan-chao5   

  1. 1. College of Science, Civil Aviation University of China, Tianjin 300300, China;
    2. Economics and Management College, Civil Aviation University of China, Tianjin 300300, China;
    3. College of Aeronautical Automation, Civil Aviation University of China, Tianjin 300300, China;
    4. Chief Engineer Office, Shandong Guoqiang Hardware Technology Cor. Ltd, Leling 253600, Shandong, China;
    5. Maintenance Management Department of Engineering Technology Company, China Eastern Airlines Cor. Ltd, Shanghai 200335, China
  • Received:2014-10-09 Revised:2015-02-11 Online:2015-11-20 Published:2015-12-09

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摘要： 利用非线性状态反馈控制法,提出了一个新的具有较大正Lyapunov指数的四维光滑自治超混沌系统。该系统具有大范围的四翼超混沌区域。讨论了系统平衡点的稳定性。通过Lyapunov指数、分岔图及Poincaré截面分析了系统的动力学行为,并用相图展示了四翼混沌吸引子和几种不同形状的四翼超混沌吸引子。随着参数的不同,该系统还可以历经拟周期和周期状态。最后给出了典型超混沌吸引子的电路实现。

关键词: 四翼吸引子, Lyapunov指数, Poincaré, 截面, 电路实现, 超混沌系统

Abstract: Using nonlinear state feedback control, a new four-dimensional smooth autonomous hyperchaotic system was constructed with large positive Lyapunov exponent. This system had larger four-wing hyperchaotic region. The stability of equilibria was discussed. The dynamic behaviors of this system were analysed through Lyapunov exponents, bifurcation diagrams and Poincaré sections. The four-wing chaotic attractor and hyperchaotic attractors were displayed by phase portraits. With various parameters, this system still underwent quasi-periodic orbits and periodic orbits. An electronic circuit is given to implement the typical hyperchaotic attractor.

Key words: Lyapunov exponent, four-wing attractor, section, circuit implementation, Poincaré, hyperchaotic system

中图分类号: 

  • O415.5
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