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吸引子涡卷数量与分布的控制:系统设计及电路实现

武花干 包伯成 刘中

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吸引子涡卷数量与分布的控制:系统设计及电路实现

武花干, 包伯成, 刘中

Scroll number and distribution control of attractor: system design and circuit realization

Liu Zhong, Wu Hua-Gan, Bao Bo-Cheng
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  • 在三维线性系统中引入两个分段线性函数,构造了一个代数方程较为简单的网格涡卷混沌系统.通过对引入的锯齿波函数和改进型锯齿波函数的零点配置,完成了该系统指数2平衡点的数量和分布设计,实现了系统所生成混沌吸引子的涡卷数量和涡卷分布的控制.利用运算放大器、乘法器等模拟元器件设计了相应的锯齿波函数电路、改进型锯齿波函数电路以及三维线性系统电路,实现了本文所提出的网格涡卷混沌系统.实验结果与理论分析和数值仿真结果一致,验证了混沌吸引子的涡卷数量和涡卷分布设计的可行性.
    Through introducing two piecewise-linear functions into a three-dimensional linear system, a grid-scroll chaotic system with relatively simple algebraic of system structure is constructed. By deploying the zero points of the introduced saw-tooth function and modified saw-tooth function, the designs of the number and the distribution of the index-2 equilibrium points of the system are performed, and the controls of the scroll number and the scroll distribution of the chaotic attractor generated from the system are achieved. By using analog components such as operational amplifier, multiplier, etc., the saw-tooth function circuit, the modified saw-tooth function circuit and the three-dimensional linear system circuit are designed and the proposed grid-scroll chaotic system is implemented. The experimental results are in agreement with both theoretical analyses and numerical simulations, which verify the feasibility of the designs of the scroll number and scroll distribution of chaotic attractors.
    • 基金项目: 国家自然科学基金(批准号:60971090)和江苏省自然科学基金(批准号:BK2009105)资助的课题.
    [1]

    Suykens J A K, Vandewalle J 1993 IEEE Trans. Circuits syst. I 40 861

    [2]

    Yalcin M E 2007 Int. J. Bifur. Chaos 174471

    [3]

    Yalcin M E, Suykens J, Vandewalle J, zoguz S 2002 Int. J. Bifur. Chaos 12 23

    [4]

    Lü J H, Yu S M, Leung H, Chen G R 2006 IEEE Trans. Circuits Syst. I 53 149

    [5]

    Lü J H, Chen G R 2006 Int. J. Bifur. Chaos 16 775

    [6]

    Yu S M, Lü J H, Chen G R 2007 IEEE Trans. Circuits Syst. I 54 2087

    [7]

    Wang F Q, Liu C X 2007 Chin. Phys. 16 942

    [8]

    Zhang C X, Yu S M 2009 Chin. Phys. B 18 119

    [9]

    Gandhi G, Roska T 2009 Int. J. Circuit Theory and Appli. 37 473

    [10]

    Bao B C, Zhou G H, Xu J P, Liu Z 2010 Int. J. Bifur. Chaos 20 2203

    [11]

    Bao B C, Liu Z, Xu J P, Zhu L 2010 Acta Phys. Sin. 59 1540 (in Chinese) [包伯成、刘 中、许建平、朱 雷 2010 物理学 报 59 1540]

    [12]

    Xu Y M, Bao B C, Xu Q 2010 Acta Phys. Sin. 59 5959 (in Chinese) [徐煜明、包伯成、徐 强 2010 物理学报 59 5959]

    [13]

    Yu S M, Tang W K S, Lü J H, Chen G R 2010 Int. J. Circuit Theory and Appli. 38 243

    [14]

    Yu S M, Tang W K S, Lü J H, Chen G R 2008 IEEE Trans. Circuits Syst. II 55 1168

    [15]

    Yalcin M, zoguz S 2007 Chaos 17 033112

    [16]

    Lü J H, Murali K, Sinha S, Leung H, Aziz-Alaoui MA 2008 Physics Letters A 372 3234

    [17]

    Mohamed I R, Murali K, Sinha S, Lindberg E 2010 Int. J. Bifur. Chaos 20 2185

    [18]

    Zhang C X, Tang W K S, Yu S M 2009 Int. J. Bifur. Chaos 19 2073

    [19]

    Chen S B, Zeng Y C, Xu M L, Chen J S 2011 Acta Phys. Sin. 60 020507 (in Chinese) [陈仕必、曾以成、徐茂林、陈家胜 2011 物理学报 60 020507]

  • [1]

    Suykens J A K, Vandewalle J 1993 IEEE Trans. Circuits syst. I 40 861

    [2]

    Yalcin M E 2007 Int. J. Bifur. Chaos 174471

    [3]

    Yalcin M E, Suykens J, Vandewalle J, zoguz S 2002 Int. J. Bifur. Chaos 12 23

    [4]

    Lü J H, Yu S M, Leung H, Chen G R 2006 IEEE Trans. Circuits Syst. I 53 149

    [5]

    Lü J H, Chen G R 2006 Int. J. Bifur. Chaos 16 775

    [6]

    Yu S M, Lü J H, Chen G R 2007 IEEE Trans. Circuits Syst. I 54 2087

    [7]

    Wang F Q, Liu C X 2007 Chin. Phys. 16 942

    [8]

    Zhang C X, Yu S M 2009 Chin. Phys. B 18 119

    [9]

    Gandhi G, Roska T 2009 Int. J. Circuit Theory and Appli. 37 473

    [10]

    Bao B C, Zhou G H, Xu J P, Liu Z 2010 Int. J. Bifur. Chaos 20 2203

    [11]

    Bao B C, Liu Z, Xu J P, Zhu L 2010 Acta Phys. Sin. 59 1540 (in Chinese) [包伯成、刘 中、许建平、朱 雷 2010 物理学 报 59 1540]

    [12]

    Xu Y M, Bao B C, Xu Q 2010 Acta Phys. Sin. 59 5959 (in Chinese) [徐煜明、包伯成、徐 强 2010 物理学报 59 5959]

    [13]

    Yu S M, Tang W K S, Lü J H, Chen G R 2010 Int. J. Circuit Theory and Appli. 38 243

    [14]

    Yu S M, Tang W K S, Lü J H, Chen G R 2008 IEEE Trans. Circuits Syst. II 55 1168

    [15]

    Yalcin M, zoguz S 2007 Chaos 17 033112

    [16]

    Lü J H, Murali K, Sinha S, Leung H, Aziz-Alaoui MA 2008 Physics Letters A 372 3234

    [17]

    Mohamed I R, Murali K, Sinha S, Lindberg E 2010 Int. J. Bifur. Chaos 20 2185

    [18]

    Zhang C X, Tang W K S, Yu S M 2009 Int. J. Bifur. Chaos 19 2073

    [19]

    Chen S B, Zeng Y C, Xu M L, Chen J S 2011 Acta Phys. Sin. 60 020507 (in Chinese) [陈仕必、曾以成、徐茂林、陈家胜 2011 物理学报 60 020507]

计量
  • 文章访问数:  5080
  • PDF下载量:  701
  • 被引次数: 0
出版历程
  • 收稿日期:  2010-11-29
  • 修回日期:  2010-12-13
  • 刊出日期:  2011-09-15

吸引子涡卷数量与分布的控制:系统设计及电路实现

  • 1. (1)常州大学信息科学与工程学院,常州 213164; (2)南京理工大学电子工程系,南京 210094
    基金项目: 

    国家自然科学基金(批准号:60971090)和江苏省自然科学基金(批准号:BK2009105)资助的课题.

摘要: 在三维线性系统中引入两个分段线性函数,构造了一个代数方程较为简单的网格涡卷混沌系统.通过对引入的锯齿波函数和改进型锯齿波函数的零点配置,完成了该系统指数2平衡点的数量和分布设计,实现了系统所生成混沌吸引子的涡卷数量和涡卷分布的控制.利用运算放大器、乘法器等模拟元器件设计了相应的锯齿波函数电路、改进型锯齿波函数电路以及三维线性系统电路,实现了本文所提出的网格涡卷混沌系统.实验结果与理论分析和数值仿真结果一致,验证了混沌吸引子的涡卷数量和涡卷分布设计的可行性.

English Abstract

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