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基于改进脉冲控制方法的超混沌系统同步

马铁东 江伟波 浮洁 薛方正

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基于改进脉冲控制方法的超混沌系统同步

马铁东, 江伟波, 浮洁, 薛方正

Synchronization of hyperchaotic systems via improved impulsive control method

Ma Tie-Dong, Jiang Wei-Bo, Fu Jie, Xue Fang-Zheng
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  • 针对一类整数阶与分数阶超混沌系统的同步问题, 分别提出了改进的脉冲同步方法. 基于Lyapunov稳定性理论与脉冲微分方程理论, 给出超混沌系统一组新的全局渐近同步判据. 特别地, 当脉冲间距与脉冲控制增益为常数时, 可获得更为简单和实用的同步判据. 与现有结果相比, 所得充分条件更次保守且更为实用. 通过对超混沌Chen系统同步的数值仿真研究, 验证了所提方法的有效性和可行性.
    The improved impulsive control method is proposed to realize the complete synchronization of integral and fractional order hyperchaotic systems. Some effective sufficient conditions are produced to realize the asymptotical stability of synchronization error system. In particular, some simple and practical conditions are derived in synchronizing the chaotic systems by choosing constant impulsive distances and control gains. Compared with the existing results, the main results are less conservative by relaxing some unnecessary inequality constraints. Simulation results show the effectiveness and the feasibility of the proposed impulsive controller.
    • 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)和中国博士后科学基金 (批准号: 20100470813, 20100480043)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), Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20100191120025), and the China Postdoctoral Science Foundation (Grant Nos. 20100470813, 20100480043).
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    Bhalekar S, Daftardar-Gejji V 2010 Commun. Nonlinear Sci. Numer. Simulat. 15 3536

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    Sheu L J, Tam L M, Lao S K, Kang Y, Lin K T, Chen J H, Chen H K 2009 Int. J. Nonlinear Sci. Numer. Simulat. 10 33

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

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

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    Zhang H G, Ma T D, Yu W, Fu J 2008 Chin. Phys. B 17 3616

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    Ma T D, Zhang H G, Wang Z L 2007 Acta Phys. Sin. 56 3796 (in Chinese) [马铁东, 张化光, 王智良 2007 物理学报 56 3796]

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    Zhang H G, Ma T D, Fu J, Tong S C 2009 Chin. Phys. B 18 3742

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    Zhang H G, Fu J, Ma T D 2009 Chin. Phys. B 18 969

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    Gao T G, Chen Z Q, Yuan Z Z, Yu D C 2007 Chaos, Solitons and Fractals 33 922

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

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    Podlubny I 1999 Fractional Differential Equations (New York: Academic)

  • [1]

    Mandelbrot B B 1983 The Fractal Geometry of Nature (New York: Freeman)

    [2]

    Hartley T T, Lorenzo C F, Qammer H K 1995 IEEE Trans. CAS-I 42 485

    [3]

    Arena P, Caponetto R, Fortuna L, Porto D 1997 Proceedings ECCTD, Budapest 42 p1259

    [4]

    Ahmad W M, Sprott J C 2003 Chaos, Solitons and Fractals 16 339

    [5]

    Yu Y G, Li H X, Wang S, Yu J Z 2009 Chaos, Solitons and Fractals 42 1181

    [6]

    Lu J G, Chen G R 2006 Chaos, Solitons and Fractals. 27 685

    [7]

    Lu J G 2006 Phys. Lett. A 354 305

    [8]

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

    [9]

    Wang X Y, He Y J 2008 Acta Phys. Sin. 57 1485 (in Chinese) [王兴元, 贺毅杰 2008 物理学报 57 1485]

    [10]

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

    [11]

    Yang D S, Zhang H G, Zhao Y, Song C H, Wang Y C 2010 Acta Phys. Sin. 59 1562 (in Chinese) [杨东升, 张化光, 赵琰, 宋崇辉, 王迎春 2010 物理学报 59 1562]

    [12]

    Zhang H G, Zhao Y, Yu W, Yang D S 2008 Chin. Phys. B 17 4056

    [13]

    Zhang H G, Huang W, Wang Z L, Chai T Y 2006 Phys. Lett. A 350 363

    [14]

    Zhang H G, Wang Z L, Liu D R 2004 Int. J. Bifurcat. Chaos 14 3505

    [15]

    Zhao Y, Zhang H G, Zheng C D 2008 Chin. Phys. B 17 529

    [16]

    Sun Q Y, Zhang H G, Zhao Y 2010 Chin. Phys. B 19 070512

    [17]

    Yang D S, Zhang H G, Li A P, Meng Z Y 2007 Acta Phys. Sin. 56 3121 (in Chinese) [杨东升, 张化光, 李爱平, 孟子怡 2007 物理学报 56 3121]

    [18]

    Wang Y C, Zhang H G, Wang X Y, Yang D S 2010 IEEE Trans. Syst. Man Cybern. B 40 1468

    [19]

    Bhalekar S, Daftardar-Gejji V 2010 Commun. Nonlinear Sci. Numer. Simulat. 15 3536

    [20]

    Taghvafard H, Erjaee G H 2011 Commun. Nonlinear Sci. Numer. Simulat. 16 4079

    [21]

    Cao H F, Zhang R X 2011 Acta Phys. Sin. 60 050510 (in Chinese) [曹鹤飞, 张若洵 2011 物理学报 60 050510]

    [22]

    Sun N, Zhang H G, Wang Z L 2011 Acta Phys. Sin. 60 050511 (in Chinese) [孙宁, 张化光, 王智良 2011 物理学报 60 050511]

    [23]

    Zhao L D, Hu J B, Liu X H 2010 Acta Phys. Sin. 59 2305 (in Chinese) [赵灵冬, 胡建兵, 刘旭辉 2010 物理学报 59 2305]

    [24]

    Odibat Z M 2010 Nonlinear Dyn. 60 479

    [25]

    Wu C J, Zhang Y B, Yang N N 2011 Chin. Phys. B 20 060505

    [26]

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

    [27]

    Sheu L J, Tam L M, Lao S K, Kang Y, Lin K T, Chen J H, Chen H K 2009 Int. J. Nonlinear Sci. Numer. Simulat. 10 33

    [28]

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

    [29]

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

    [30]

    Zhang H G, Ma T D, Yu W, Fu J 2008 Chin. Phys. B 17 3616

    [31]

    Ma T D, Zhang H G, Wang Z L 2007 Acta Phys. Sin. 56 3796 (in Chinese) [马铁东, 张化光, 王智良 2007 物理学报 56 3796]

    [32]

    Zhang H G, Ma T D, Fu J, Tong S C 2009 Chin. Phys. B 18 3742

    [33]

    Zhang H G, Fu J, Ma T D 2009 Chin. Phys. B 18 969

    [34]

    Zhang H G, Ma T D, Fu J, Tong S C 2009 Chin. Phys. B 18 3751

    [35]

    Gao T G, Chen Z Q, Yuan Z Z, Yu D C 2007 Chaos, Solitons and Fractals 33 922

    [36]

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

    [37]

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

    [38]

    Podlubny I 1999 Fractional Differential Equations (New York: Academic)

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出版历程
  • 收稿日期:  2011-09-21
  • 修回日期:  2012-05-28
  • 刊出日期:  2012-05-05

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