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一类分数阶混沌系统的自适应同步

马铁东 江伟波 浮洁 柴毅 陈立平 薛方正

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一类分数阶混沌系统的自适应同步

马铁东, 江伟波, 浮洁, 柴毅, 陈立平, 薛方正

Adaptive synchronization of a class of fractional-order chaotic systems

Ma Tie-Dong, Jiang Wei-Bo, Fu Jie, Chai Yi, Chen Li-Ping, Xue Fang-Zheng
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  • 针对一类分数阶混沌系统的同步问题,基于分数阶系统的类Lyapunov稳定性理论,设计了一种新的自适应同步控制器以及控制增益系数自适应律.与现有结果相比,该方法具有控制器结构简单、控制代价小以及通用性强等特点,可适用于大部分典型的分数阶混沌系统.最后,数值仿真结果验证了所提方法运用于分数阶混沌系统同步研究的有效性.
    In view of chaos synchronization of a class of fractional-order chaotic systems, a novel adaptive controller and adaptive updating law are designed based on the quasi-Lyapunov stability theory for fractional-order systems. The derived method has some advantages such as simple structure, low control cost and high generality compared with the existing results. Furthermore, the method can be applied to most typical fractional-order chaotic systems. Finally, numerical simulations are used to illustrate the effectiveness of the proposed synchronization method.
    • 基金项目: 国家自然科学基金(批准号: 61104080); 重庆市自然科学基金(批准号:CSTC, 2010BB2238); 教育部博士点基金(批准号: 20100191120025); 中国博士后科学基金(批准号: 20100470813,20100480043)和中央高校基本科研业务费(批准号: CDJXS12170005)资助的课题.
    • Funds: Project supported by the National Natural Science Foundation of China (Grant No. 61104080), the Natural Science Foundation of Chongqing, China (Grant No. CSTC, 2010BB2238), the Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20100191120025), the China Postdoctoral Science Foundation (Grant Nos. 20100470813, 20100480043), and the Fundamental Research Fund for the Central Universities, China (Grant No. CDJXS12170005).
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    Wu Z M, Xie J Y 2007 Chin. Phys. 16 1901

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    Fu J, Yu M, Ma T D 2011 Chin. Phys. B 20 120508

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    Hu J B, Han Y, Zhao L D 2007 Acta Phys. Sin. 58 2235 (in Chinese) [胡建兵,韩焱,赵灵冬 2009 物理学报 58 2235]

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    Lu J G 2005 Chaos Soliton. Fract. 26 1125

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    Gao T G, Chen Z Q, Yuan Z Z, Yu D C 2007 Chaos Soliton. Fract. 33 922

  • [1]
    [2]

    Gao X, Yu J B 2005 Chin. Phys. 14 908

    [3]
    [4]

    Lu J G 2006 Physica A 359 107

    [5]

    Yu Y G, Li H X, Wang S 2009 Chaos Soliton. Fract. 42 1181

    [6]
    [7]
    [8]

    Li C G, Chen G R 2004 Physica A 341 55

    [9]
    [10]

    Lu J G 2006 Phys. Lett. A 354 305

    [11]
    [12]

    Pecora L M, Carroll T L 1990 Phys. Rev. Lett. 64 821

    [13]
    [14]

    Zhang H G, Ma T D, Huang G B, Wang Z L 2010 IEEE Trans. Syst. Man Cybern. B 40 831

    [15]
    [16]

    Wang M J, Wang X Y 2011 Int. J. Mod. Phys. B 25 1283

    [17]
    [18]

    Ma T D, Fu J, Sun Y 2010 Chin. Phys. B 19 090502

    [19]
    [20]

    Wang X Y, Liu R, Zhang N 2011 Commun. Theor. Phys. 55 617

    [21]

    Zhang R X, Yang Y, Yang S P 2009 Acta Phys. Sin. 58 6039 (in Chinese) [张若洵,杨洋,杨世平 2009 物理学报 58 6039]

    [22]
    [23]

    Chen L P, Chai Y, Wu R C 2011 Phys. Lett. A 375 2099

    [24]
    [25]

    Wang M J, Wang X Y, Niu Y J 2011 Chin. Phys. B 20 010508

    [26]
    [27]
    [28]

    Wang X Y, Zhang Y L, Lin D, Zhang N 2011 Chin. Phys. B 20 030506

    [29]

    Niu Y J, Wang X Y, Nian F Z, Wang M J 2010 Chin. Phys. B 19 120507

    [30]
    [31]
    [32]

    Jia L X, Dai H, Hui M 2010 Chin. Phys. B 19 110509

    [33]

    Chen X R, Liu C X, Wang F Q, Li Y X 2008 Acta Phys. Sin. 57 1416 (in Chinese) [陈向荣,刘崇新,王发强,李永勋 2008 物理学报 57 1416]

    [34]
    [35]

    Min F H, Yu Y, Ge C J 2009 Acta Phys. Sin. 58 1456 (in Chinese) [闵富红, 余杨, 葛曹君 2009 物理学报 58 1456]

    [36]
    [37]
    [38]

    Wu Z M, Xie J Y 2007 Chin. Phys. 16 1901

    [39]

    Fu J, Yu M, Ma T D 2011 Chin. Phys. B 20 120508

    [40]
    [41]

    Hu J B, Han Y, Zhao L D 2007 Acta Phys. Sin. 58 2235 (in Chinese) [胡建兵,韩焱,赵灵冬 2009 物理学报 58 2235]

    [42]
    [43]
    [44]

    Matignon D 1996 IMACS, IEEE SMC Proceedings Conference Lille, France, July 9-12, 1996 p963

    [45]
    [46]

    Lu J G 2005 Chaos Soliton. Fract. 26 1125

    [47]

    Gao T G, Chen Z Q, Yuan Z Z, Yu D C 2007 Chaos Soliton. Fract. 33 922

计量
  • 文章访问数:  5800
  • PDF下载量:  4855
  • 被引次数: 0
出版历程
  • 收稿日期:  2011-12-19
  • 修回日期:  2012-01-15
  • 刊出日期:  2012-08-05

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