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噪声诱导的二维复时空系统的同步研究

都琳 徐伟 许勇 王亮

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噪声诱导的二维复时空系统的同步研究

都琳, 徐伟, 许勇, 王亮

Noise-induced synchronization of two-dimensional complex spatiotemporal systems

Du Lin, Xu Wei, Xu Yong, Wang Liang
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  • 研究了一类噪声诱导的二维复时空系统的同步问题.首先讨论了二维复Ginzburg-Laudau(CGL) 方程随时间和空间变化的时空混沌特性;其次,研究了时空噪声驱动下CGL系统的同步问题.理论上利用线性稳定性分析,得到了常数激励下CGL系统达到稳定态的临界强度;结合噪声的随机性和非零均值特性, 揭示了噪声诱导同步的机理;并从理论上和数值上分别给出了达到同步所需要的控制参数和噪声强度满足的条件,实现了两个非耦合CGL系统的完全同步.结果表明,数值模拟和理论分析有很好的一致性.
    A type of noise-induced synchronization in two-dimensional (2D) complex spatiotemporal system is studied in this paper. First, we employ a 2D complex Ginzburg-Laudau equation (CGL) to present spatiotemporal chaos. Then the synchronization in the CGL equation driven by spatiotemporal noise is studied. Theoretically, the critical control intensity is obtained by linear stability analysis of a constant forced CGL system. Combining with randomness and non-zero mean of the noise, we reveal the mechanism of synchronization and give the required conditions for control parameters and noise intensity resulting in synchronization theoretically and numerically. A complete synchronization in a pair of uncoupled CGL equations is achieved. A good agreement between the theoretical analyses and the numerical results is obtained.
    • 基金项目: 国家自然科学基金(批准号: 11172233, 10902085, 10972181)、西北工业大学基础研究基金、翱翔之星和博士论文创新基金资助的课题.
    • Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 11172233, 10902085, 10972181), the Fundamental Research Fund, Aoxiang Star Plan and the Doctorate Foundation of Northwestern Polytechnical University, China.
    [1]

    Hu G, Xiao J H, Zheng Z G 2000 Chaos Control (Shanghai: Shanghai Scientific and Technological Press) pp78-148 (in Chinese) [胡岗, 萧井华, 郑志刚 2000 混沌控制 (上海: 上海科技教育出版社)第78-第148页

    [2]

    Jia F L, Xu W, Du L 2007 Acta Phys. Sin. 56 5640 (in Chinese) [贾飞蕾, 徐伟, 都琳 2007 物理学报 56 5640]

    [3]

    Lü L, Li G, Chai Y 2008 Acta Phys. Sin. 57 7517 (in Chinese) [吕翎, 李钢, 柴元 2008 物理学报 57 7517]

    [4]

    Ahlborn A, Parlitz U 2008 Phys. Rev. E 77 016201

    [5]

    Wang X Y, Zhang N, Ren X L, Zhang Y L 2011 Chin. Phys. B 20 020507

    [6]

    Hramov A E, Koronovskii A A, Popov P V 2005 Phys. Rev. E 72 037201

    [7]

    Hramov A E, Koronovskii A A, Popov P V 2008 Phys. Rev. E 77 036215

    [8]

    Goldobin D S, Pikovsky A 2005 Phys. Rev. E 71 045201(R)

    [9]

    Hramov A E, Koronovskii A A, Popov P V, Moskalenko O I 2006 Phys. Lett. A 354 423

    [10]

    Hu A H, Xu Z Y 2007 Acta Phys. Sin. 56 3132 (in Chinese) [胡爱花, 徐振源 2007 物理学报 56 3132]

    [11]

    Moskalenko O L, Koronovskii A A, Hramov A E 2010 Phys. Lett. A 374 2925

    [12]

    Guo B L, Huang H Y 2003 Ginzburg-Laudau Equation (Beijing: Science Press) pp121-130 (in Chinese) [郭柏灵, 黄海洋 2002 金兹堡-朗道方程 (北京: 科学出版社) 第121-130页]

    [13]

    Aranson I S, Kramer L 2002 Rev. Modern Phys. 74 100

    [14]

    Du L, Xu W, Li Z, Zhou B 2011 Phys. Lett. A 375 1870

    [15]

    Bartuccelli M, Constantin P, Doering C R 1990 Physica D 44 421

    [16]

    Gao J L, Xie L L, Peng J H 2009 Acta Phys. Sin. 58 5218 (in Chinese) [高继华, 谢玲玲, 彭建华 2009 物理学报 58 5218]

    [17]

    Chate H, Pikovsky A S, Rudzick O 1999 Physica D 131 17

    [18]

    Ouyang Q 2010 Introduction of Nonlinear Science and Pattern Dynamics (Beijing: Beijing University Press) pp140-142 (in Chinese) [欧阳颀 2010 非线性科学与斑图动力学导论 (第二版) (北京: 北京大学出版社) 第140-142页]

  • [1]

    Hu G, Xiao J H, Zheng Z G 2000 Chaos Control (Shanghai: Shanghai Scientific and Technological Press) pp78-148 (in Chinese) [胡岗, 萧井华, 郑志刚 2000 混沌控制 (上海: 上海科技教育出版社)第78-第148页

    [2]

    Jia F L, Xu W, Du L 2007 Acta Phys. Sin. 56 5640 (in Chinese) [贾飞蕾, 徐伟, 都琳 2007 物理学报 56 5640]

    [3]

    Lü L, Li G, Chai Y 2008 Acta Phys. Sin. 57 7517 (in Chinese) [吕翎, 李钢, 柴元 2008 物理学报 57 7517]

    [4]

    Ahlborn A, Parlitz U 2008 Phys. Rev. E 77 016201

    [5]

    Wang X Y, Zhang N, Ren X L, Zhang Y L 2011 Chin. Phys. B 20 020507

    [6]

    Hramov A E, Koronovskii A A, Popov P V 2005 Phys. Rev. E 72 037201

    [7]

    Hramov A E, Koronovskii A A, Popov P V 2008 Phys. Rev. E 77 036215

    [8]

    Goldobin D S, Pikovsky A 2005 Phys. Rev. E 71 045201(R)

    [9]

    Hramov A E, Koronovskii A A, Popov P V, Moskalenko O I 2006 Phys. Lett. A 354 423

    [10]

    Hu A H, Xu Z Y 2007 Acta Phys. Sin. 56 3132 (in Chinese) [胡爱花, 徐振源 2007 物理学报 56 3132]

    [11]

    Moskalenko O L, Koronovskii A A, Hramov A E 2010 Phys. Lett. A 374 2925

    [12]

    Guo B L, Huang H Y 2003 Ginzburg-Laudau Equation (Beijing: Science Press) pp121-130 (in Chinese) [郭柏灵, 黄海洋 2002 金兹堡-朗道方程 (北京: 科学出版社) 第121-130页]

    [13]

    Aranson I S, Kramer L 2002 Rev. Modern Phys. 74 100

    [14]

    Du L, Xu W, Li Z, Zhou B 2011 Phys. Lett. A 375 1870

    [15]

    Bartuccelli M, Constantin P, Doering C R 1990 Physica D 44 421

    [16]

    Gao J L, Xie L L, Peng J H 2009 Acta Phys. Sin. 58 5218 (in Chinese) [高继华, 谢玲玲, 彭建华 2009 物理学报 58 5218]

    [17]

    Chate H, Pikovsky A S, Rudzick O 1999 Physica D 131 17

    [18]

    Ouyang Q 2010 Introduction of Nonlinear Science and Pattern Dynamics (Beijing: Beijing University Press) pp140-142 (in Chinese) [欧阳颀 2010 非线性科学与斑图动力学导论 (第二版) (北京: 北京大学出版社) 第140-142页]

计量
  • 文章访问数:  6245
  • PDF下载量:  489
  • 被引次数: 0
出版历程
  • 收稿日期:  2011-09-18
  • 修回日期:  2011-11-18
  • 刊出日期:  2012-03-05

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