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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.
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Keywords:
- synchronization /
- noise /
- spatiotemporal chaos /
- complex Ginzburg-Laudau equation
[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 56 5640]
[3] Lü L, Li G, Chai Y 2008 Acta Phys. Sin. 57 7517 (in Chinese) [吕翎, 李钢, 柴元 2008 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 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 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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[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 56 5640]
[3] Lü L, Li G, Chai Y 2008 Acta Phys. Sin. 57 7517 (in Chinese) [吕翎, 李钢, 柴元 2008 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 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 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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