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Chin. Phys. B, 2011, Vol. 20(12): 120505    DOI: 10.1088/1674-1056/20/12/120505
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Generalized spatiotemporal chaos synchronization of the Ginzburg–Landau equation

Jin Ying-Hua(金英花)a)† and Xu Zhen-Yuan(徐振源)b)
a School of Sciences, Jiangnan University, Wuxi 214122, China; b School of Information Technology, Jiangnan University, Wuxi 214122, China
Abstract  In this paper, the generalized synchronization of two unidirectionally coupled Ginzburg-Landau equations is studied theoretically. It is demonstrated that the drive-response system has bounded attraction domain and compact attractors. It is derived that the correction equation has asymptotically stable zero solutions under certain conditions and that the sufficient conditions for smooth generalized synchronization and Hölder continuous generalized synchronization exist in the coupling system. Numerical result analysis shows the correctness of theory.
Keywords:  generalized synchronization manifold      Ginzburg-Landau equation      spatiotemporal chaos      attractor  
Received:  14 January 2011      Revised:  30 June 2011      Accepted manuscript online: 
PACS:  05.45.Xt (Synchronization; coupled oscillators)  
Fund: Project supported by the Fundamental Research Funds for the Central Universities (Grant No. JUSRP211A21) and the National Natural Science Foundation of China (Grant No. 11002061).

Cite this article: 

Jin Ying-Hua(金英花) and Xu Zhen-Yuan(徐振源) Generalized spatiotemporal chaos synchronization of the Ginzburg–Landau equation 2011 Chin. Phys. B 20 120505

[1] Corroll T L and Pecora L M 1990 Phys. Rev. Lett. 64 821
[2] Abarbanel H D I, Rulkov N F and Sushchik M M 1996 Phys. Rev. 53 4528
[3] Pikovsky A, Rosenblum M and Kurths J 2001 Synchronization: A Universal Concept in Nonlinear Sciences (Cambridge: Cambridge University Press)
[4] Kiss I Z, Hudson J L, Escalona J and Parmananda P 2004 Phys. Rev. E 70 026210
[5] Prokhorov M D, Ponomarenko V I, Gridnev V I, Bodrov M B and Bespyatov A B 2003 Phys. Rev. E 68 041913
[6] Duane G S and Tribbia J J 2001 Phys. Rev. Lett. 86 4298
[7] Wei G W 2001 Phys. Rev. Lett. 86 3542
[8] Guo L X, Xu Z Y and Hu A H 2011 Chin. Phys. B 20 010507
[9] Zhang Q L and Lu L 2011 Chin. Phys. B 20 010510
[10] Wang X Y, Zhang N, Ren X L and Zhang Y L 2011 Chin. Phys. B 20 020507
[11] Junge L and Parlitz U 2000 Phys. Rev. E 62 438
[12] Tasev Z, Kocarev L, Junge L and Parlitz U 2000 J. Bifur. Chaos 10 869
[13] Koronovskii A A, Popov P V and Hramov A E 2006 Physica 103 654
[14] Rulkov N, Sushchik M M and Tsimring L S 1995 Phys. Rev. E 51 980
[15] Xu G Z, Gu J F and Che H A 2000 System Science (Shanghai: Shanghai Scientific and Technological Education Publishing House) (in Chinese)
[16] Temam R 1988 Appl. Math. Ser. (New York: Springer-Verlag) Vol. 68
[17] Li Y, Mclaughlin D, Sharah J and Wiggins S 1996 Comm. Pure Appl. Math. 49 1175
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