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Noise-induced synchronization of two-dimensional complex spatiotemporal systems

Du Lin Xu Wei Xu Yong Wang Liang

Noise-induced synchronization of two-dimensional complex spatiotemporal systems

Du Lin, Xu Wei, Xu Yong, Wang Liang
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  • 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.
    • 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]

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    [4] Lü Ling, Jing Xiao-Dan. The synchronization of spatiotemporal chaos of all-to-all network using nonlinear coupling. Acta Physica Sinica, 2009, 58(11): 7539-7543. doi: 10.7498/aps.58.7539
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    [6] Lü Ling, Li Gang, Shang Jin-Yu, Shen Na, Zhang Xin, Liu Shuang, Zhu Jia-Bo. The synchronization of spatiotemporal chaos of nearest-neighbor coupled network. Acta Physica Sinica, 2010, 59(9): 5966-5971. doi: 10.7498/aps.59.5966
    [7] Lü Ling, Li Gang, Zhang Meng, Li Yu-Shan, Wei Lin-Ling, Yu Miao. Parameter identification and synchronization of spatiotemporal chaos in globally coupled network. Acta Physica Sinica, 2011, 60(9): 090505. doi: 10.7498/aps.60.090505
    [8] Lü Ling, Li Gang, Chai Yuan. The synchronization of spatiotemporal chaos of unilateral coupled map lattice. Acta Physica Sinica, 2008, 57(12): 7517-7521. doi: 10.7498/aps.57.7517
    [9] Luan Ling, Li Yan, Lü Ling. Lag synchronization of spatiotemporal chaos in a weighted network with ring connection. Acta Physica Sinica, 2009, 58(7): 4463-4468. doi: 10.7498/aps.58.4463
    [10] Lü Ling, Meng Le, Guo Li, Zou Jia-Rui, Yang Ming. Projective synchronization of a weighted network in a laser spatiotemporal chaos model. Acta Physica Sinica, 2011, 60(3): 030506. doi: 10.7498/aps.60.030506
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  • Received Date:  18 September 2011
  • Accepted Date:  18 November 2011
  • Published Online:  05 March 2012

Noise-induced synchronization of two-dimensional complex spatiotemporal systems

  • 1. Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an 710072, China
Fund Project:  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.

Abstract: 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.

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