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时滞复Lorenz混沌系统特性及其自时滞同步

张芳芳 刘树堂 余卫勇

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时滞复Lorenz混沌系统特性及其自时滞同步

张芳芳, 刘树堂, 余卫勇

Characteristics of time-delay complex Lorenz chaotic system and its self-synchronization of time delay

Zhang Fang-Fang, Liu Shu-Tang, Yu Wei-Yong
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  • 自时滞同步是指保持混沌系统结构和参数不变的情况下, 使时滞系统和原系统同步, 从而避免了现实中因为时滞而产生的各种问题. 本文以时滞复Lorenz系统为例, 研究其动态特性及时滞因数的影响, 并提出了一种非线性反馈控制器实现了复Lorenz系统的自时滞混沌同步. 数值仿真结果验证了该控制器的有效性. 该控制器只对部分状态进行控制, 实现了所有状态的同步, 原理简单, 易于工程实现.
    Self-synchronization of time delay implies that the synchronization between the time-delay system and the original system keeps the structure and parameters of systems unchanged, thus these various problems produced by time-delay in practice are avoided. Taking a time-delay complex Lorenz system for example, we investigate its dynamic characteristics and the influence of of time lag factor. A nonlinear feedback controller is designed to realize the self-synchronization of time delay of the complex Lorenz system. Numerical simulations verify the effectiveness of the presented controller. The controller adopts some states to realize the synchronization of all states. It is simple in principle and easy to implement in engineering.
    • 基金项目: 国家自然科学基金(批准号: 61273088, 10971120, 61001099)和山东省自然科学基金(批准号: ZR2010FM010)资助的课题.
    • Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 61273088, 10971120, 61001099) and the Nature Science Foundation of Shandong Province, China (Grant No. ZR2010FM010).
    [1]

    Liang Y, Wang X Y 2013 Acta Phys. Sin. 62 018901 (in Chinese) [梁义, 王兴元 2013 物理学报 62 018901]

    [2]

    Ouyang C, Lin W T, Cheng R J, Mo J Q 2013 Acta Phys. Sin. 62 060201 (in Chinese) [欧阳成, 林万涛, 程荣军, 莫嘉琪 2013 物理学报 62 060201]

    [3]

    Li C D, Liao X F 2004 Phys. Lett. A 329 301

    [4]

    Jia F L, Xu W 2007 Acta Phys. Sin. 56 3101 (in Chinese) [贾飞蕾, 徐伟 2007 物理学报 56 3101]

    [5]

    Mahmoud G M, Mahmoud E E 2012 Nonlinear Dyn. 67 1613

    [6]

    Wang X Y, Zhang H 2013 Chin. Phys. B 22 048902

    [7]

    Fowler A C, Gibbon J D 1982 Physica D 4 139

    [8]

    Mahmoud G M, Bountis T, Mahmoud E E 2007 Internat. J. Bifur. Chaos 17 4295

    [9]

    Luo C, Wang X Y 2013 Nonlinear Dyn. 71 241

    [10]

    Luo C, Wang X Y 2013 Int. J. Mod. Phys. C 24 1350025

    [11]

    Mahmoud G M, Mahmoud E E 2010 Nonlinear Dyn. 61 141

    [12]

    Nian F Z, Wang X Y, Niu Y J, Lin D 2010 Appl. Math. Comput. 217 2481

    [13]

    Mahmoud G M, Mahmoud E E 2010 Nonlinear Dyn. 62 875

    [14]

    Liu S T, Liu P 2011 Nonlinear Anal. Real 12 3046

    [15]

    Liu P, Liu S T 2011 Phys. Scr. 83 065006

    [16]

    Mahmoud G M, Mahmoud E E 2010 Math. Comput. Simulat. 80 2286

    [17]

    Liu P, Liu S 2012 Nonlinear Dyn. 70 585

    [18]

    Zhu H 2011 ICCRD: 3rd Int. Conf. on Computer Research Development Shanghai, China, March 11–13, 2011 p451

    [19]

    Liu P, Liu S T, Li X 2012 Phys. Scr. 85 035005

    [20]

    Mahmoud E E 2013 Math. Comput. Simulat. 89 69

    [21]

    Zhang F F, Liu S T, Yu W Y 2013 Chin. Phys. B 22 120505

    [22]

    Gibbon J D, McGuinnes M J 1982 Physica D 5 108

    [23]

    Ning C Z, Haken H 1990 Phys. Rev. A 41 3826

    [24]

    Rauh A, Hannibal L, Abraham N 1996 Physica D 99 45

    [25]

    Richter H 2001 Chaos Soliton. Fract. 12 2375

    [26]

    Wolf A, Swift J B, Swinney H L, Vastano J A 1985 Physica D 16 285

    [27]

    Hale J 1977 Theory of Functional Differential Equations (Vol. 3) (Berlin: Springer-Verlag) pp1–244

  • [1]

    Liang Y, Wang X Y 2013 Acta Phys. Sin. 62 018901 (in Chinese) [梁义, 王兴元 2013 物理学报 62 018901]

    [2]

    Ouyang C, Lin W T, Cheng R J, Mo J Q 2013 Acta Phys. Sin. 62 060201 (in Chinese) [欧阳成, 林万涛, 程荣军, 莫嘉琪 2013 物理学报 62 060201]

    [3]

    Li C D, Liao X F 2004 Phys. Lett. A 329 301

    [4]

    Jia F L, Xu W 2007 Acta Phys. Sin. 56 3101 (in Chinese) [贾飞蕾, 徐伟 2007 物理学报 56 3101]

    [5]

    Mahmoud G M, Mahmoud E E 2012 Nonlinear Dyn. 67 1613

    [6]

    Wang X Y, Zhang H 2013 Chin. Phys. B 22 048902

    [7]

    Fowler A C, Gibbon J D 1982 Physica D 4 139

    [8]

    Mahmoud G M, Bountis T, Mahmoud E E 2007 Internat. J. Bifur. Chaos 17 4295

    [9]

    Luo C, Wang X Y 2013 Nonlinear Dyn. 71 241

    [10]

    Luo C, Wang X Y 2013 Int. J. Mod. Phys. C 24 1350025

    [11]

    Mahmoud G M, Mahmoud E E 2010 Nonlinear Dyn. 61 141

    [12]

    Nian F Z, Wang X Y, Niu Y J, Lin D 2010 Appl. Math. Comput. 217 2481

    [13]

    Mahmoud G M, Mahmoud E E 2010 Nonlinear Dyn. 62 875

    [14]

    Liu S T, Liu P 2011 Nonlinear Anal. Real 12 3046

    [15]

    Liu P, Liu S T 2011 Phys. Scr. 83 065006

    [16]

    Mahmoud G M, Mahmoud E E 2010 Math. Comput. Simulat. 80 2286

    [17]

    Liu P, Liu S 2012 Nonlinear Dyn. 70 585

    [18]

    Zhu H 2011 ICCRD: 3rd Int. Conf. on Computer Research Development Shanghai, China, March 11–13, 2011 p451

    [19]

    Liu P, Liu S T, Li X 2012 Phys. Scr. 85 035005

    [20]

    Mahmoud E E 2013 Math. Comput. Simulat. 89 69

    [21]

    Zhang F F, Liu S T, Yu W Y 2013 Chin. Phys. B 22 120505

    [22]

    Gibbon J D, McGuinnes M J 1982 Physica D 5 108

    [23]

    Ning C Z, Haken H 1990 Phys. Rev. A 41 3826

    [24]

    Rauh A, Hannibal L, Abraham N 1996 Physica D 99 45

    [25]

    Richter H 2001 Chaos Soliton. Fract. 12 2375

    [26]

    Wolf A, Swift J B, Swinney H L, Vastano J A 1985 Physica D 16 285

    [27]

    Hale J 1977 Theory of Functional Differential Equations (Vol. 3) (Berlin: Springer-Verlag) pp1–244

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  • PDF下载量:  792
  • 被引次数: 0
出版历程
  • 收稿日期:  2013-05-13
  • 修回日期:  2013-08-02
  • 刊出日期:  2013-11-05

时滞复Lorenz混沌系统特性及其自时滞同步

  • 1. 山东大学控制科学与工程学院, 济南 250061
    基金项目: 国家自然科学基金(批准号: 61273088, 10971120, 61001099)和山东省自然科学基金(批准号: ZR2010FM010)资助的课题.

摘要: 自时滞同步是指保持混沌系统结构和参数不变的情况下, 使时滞系统和原系统同步, 从而避免了现实中因为时滞而产生的各种问题. 本文以时滞复Lorenz系统为例, 研究其动态特性及时滞因数的影响, 并提出了一种非线性反馈控制器实现了复Lorenz系统的自时滞混沌同步. 数值仿真结果验证了该控制器的有效性. 该控制器只对部分状态进行控制, 实现了所有状态的同步, 原理简单, 易于工程实现.

English Abstract

参考文献 (27)

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