Hölder continuity of generalized chaos synchronization in complex networks

doi:10.1088/1674-1056/20/9/090511

Abstract A complex network consisting of chaotic systems is considered and the existence of the Hölder continuous generalized synchronization in the network is studied. First, we divide nodes of the network into two parts according to their dynamical behaviour. Then, based on the Schauder fixed point theorem, sufficient conditions for the existence of the generalized synchronization between them are derived. Moreover, the results are theoretically proved. Numerical simulations validate the theory.

Keywords: generalized synchronization H?lder continuity Schauder fixed point chaotic system

Received: 16 February 2011
Revised: 17 April 2011
Accepted manuscript online:

PACS:

05.45.Xt

(Synchronization; coupled oscillators)

Cite this article:

Hu Ai-Hua(胡爱花), Xu Zhen-Yuan(徐振源), and Guo Liu-Xiao(过榴晓) Hölder continuity of generalized chaos synchronization in complex networks 2011 Chin. Phys. B 20 090511

[1]	Pecora L M and Carroll T L 1990 Phys. Rev. Lett. 64 821
[2]	Lu J Q and Cao J D 2007 Physica A 382 672
[3]	Hu M F and Xu Z Y 2008 Nonlinear Anal. Real World Appl. 9 1253
[4]	Zhou J, Xiang L and Liu Z R 2007 Physica A 384 684
[5]	Wu J S and Jiao L C 2008 Physica A 387 2111
[6]	Lu J Q and Cao J D 2007 Nonlinear Anal. Real World Appl. 8 1252
[7]	Li R H, Chen W S and Li S 2010 Chin. Phys. B 19 010508
[8]	Fu S H and Pei L J 2010 Acta Phys. Sin. 59 5985 (in Chinese)
[9]	Liu Y Z, Jiang C S and Lin C S 2007 Acta Phys. Sin. 56 707 (in Chinese)
[10]	Hu A H and Xu Z Y 2008 Phys. Lett. A 372 3814
[11]	González-Miranda J M 2002 Phys. Rev. E 65 047202
[12]	Uchida A, McAllister R, Meucci R and Roy R 2003 Phys. Rev. Lett. 91 174101
[13]	Rogers E, Kalra R, Schroll R, Uchida A, Lathrop D P and Roy R 2004 Phys. Rev. Lett. 93 084101
[14]	Li G H 2007 Chin. Phys. 16 2608
[15]	Rulkov N F, Sushchik M M and Tsimring L S 1995 Phys. Rev. E 51 980
[16]	Abarbanel H D I, Rulkov N F and Sushchik M M 1996 Phys. Rev. E 53 4528
[17]	Kocarev L and Parlitz U 1996 Phys. Rev. Lett. 76 1816
[18]	Hramov A E and Koronovskii A A 2005 Phys. Rev. E 71 067201
[19]	Li F, Hu A H and Xu Z Y 2006 Acta Phys. Sin. 55 590 (in Chinese)
[20]	Guo L X and Xu Z Y 2008 Acta Phys. Sin. 57 6086 (in Chinese)
[21]	Hu A H, Xu Z Y and Guo L X 2009 Acta Phys. Sin. 58 6030 (in Chinese)
[22]	Zhang R and Xu Z Y 2008 J. Sys. Sci. Math. Scis. 28 1509 (in Chinese)
[23]	Guo L X and Xu Z Y 2008 Chaos 18 033134
[24]	Hu A H, Xu Z Y and Guo L X 2009 Nonlinear Anal. Theory Methods Appl. 71 5994
[25]	Hu A H, Xu Z Y and Guo L X 2009 Phys. Lett. A 373 2319
[26]	Wu J S and Jiao L C 2008 Physica D 237 2487
[27]	Wu J S and Jiao L C 2008 IEEE Trans. Circ. Syst. II 55 932
[28]	Zhang Q L and Lü L 2011 Chin. Phys. B 20 010510
[29]	Qi W and Wang Y H 2009 Chin. Phys. B 18 1404
[30]	Hung Y C, Huang Y T, Ho M C and Hu C K 2008 Phys. Rev. E 77 016202
[31]	Wang R H and Wu Q Z 1979 Lectures on Ordinary Differential Equations (Beijing: Peopel Eduation Press) (in Chinese)
[32]	Ling Z S 1986 Almost Periodic Differential Equation and Integral Manifold (Shanghai: Shanghai Science and Technology Press) (in Chinese)

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Hölder continuity of generalized chaos synchronization in complex networks

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