A new kind of nonlinear phenomenon in coupled fractional-order chaotic systems: coexistence of anti-phase and complete synchronization

doi:10.1088/1674-1056/20/8/080503

Abstract In this paper, we have found a kind of interesting nonlinear phenomenon—-hybrid synchronization in linearly coupled fractional-order chaotic systems. This new synchronization mechanism, i.e., part of state variables are anti-phase synchronized and part completely synchronized, can be achieved using a single linear controller with only one drive variable. Based on the stability theory of the fractional-order system, we investigated the possible existence of this new synchronization mechanism. Moreover, a helpful theorem, serving as a determinant for the gain of the controller, is also presented. Solutions of coupled systems are obtained numerically by an improved Adams—Bashforth—Moulton algorithm. To support our theoretical analysis, simulation results are given.

Keywords: fractional-order unified chaotic system hybrid synchronization linear controller single drive variable

Received: 26 February 2011
Revised: 25 April 2011
Accepted manuscript online:

PACS:

05.45.-a

(Nonlinear dynamics and chaos)

Fund: Project supported by the National Natural Science Foundation of China (Grant No. 60973097).

Cite this article:

Zhang Jun-Feng(张俊峰), Pei Qiu-Yu(裴秋雨), and Zhang Xiao-Li(张晓丽) A new kind of nonlinear phenomenon in coupled fractional-order chaotic systems: coexistence of anti-phase and complete synchronization 2011 Chin. Phys. B 20 080503

[1]	Gao X and Yu J B 2005 Chaos, Solitons and Fractals 26 1125
[2]	Hartley T T, Lorenzo C F and Qammer H K 1995 IEEE Trans. Circuit Syst. Theor. Appl. 42 485
[3]	Li C P and Peng G J 2004 Chaos, Solitons and Fractals 20 443
[4]	Lu J G 2006 Phys. Lett. A 354 305
[5]	Wang J W and Zhang Y B 2006 Chaos, Solitons and Fractals 30 1265
[6]	Grigorenko I and Grigorenko E 2003 Phys. Rev. Lett. 91 034101
[7]	Li C G and Chen G R 2004 Physica A 341 55
[8]	Pecora L M and Carroll T L 1990 Phys. Rev. Lett. 64 821
[9]	Maritan A and Banavar J 1994 Phys. Rev. Lett. 72 1451
[10]	Zhang R X, Yang S P and Liu Y L 2009 Acta Phys. Sin. 58 6039 (in Chinese)
[11]	Rosenblum M G, Pikovsky A S and Kurths J 1996 Phys. Rev. Lett. 76 1804
[12]	Volodchenko K, Ivanov V N, Gong S H, Choi M, Park Y J and Kim C M 2001 Opt. Lett. 26 1406
[13]	Pyragas K 2002 Phys. Rev. E 54 4508
[14]	Gonzalez-Miranda J M 2002 Phys. Rev. E 65 047202
[15]	Li C D, Chen Q and Huang T W 2008 Chaos, Solitons and Fractals 38 461
[16]	Podlubny I 1999 Fractional Differential Equations (New York: Academic Press)
[17]	Ahmad W M and Sprott J C 2003 Chaos, Solitons and Fractals 16 339
[18]	Samko S G, Klibas A A and Marichev O I 1993 Fractional Integrals and Derivatives: Theory and Applications (Amsterdam: Gordan and Breach)
[19]	Wu X J, Li J and Chen G R 2008 J. Fran. Inst. 345 392
[20]	Lü J H, Chen G R, Cheng D Z and Celikovsky S 2002 Int. J. Bifur. Chaos 12 2917
[21]	Zhang R X, Yang S P and Liu Y L 2010 Acta Phys. Sin. 59 1549 (in Chinese)
[22]	Li J F, Li N and Chen C X 2010 Acta Phys. Sin. 59 7644 (in Chinese)
[23]	Chen X R, Liu C X and Wang F Q 2008 Chin. Phys. B 17 1664
[24]	Hu J and Zhang Q J 2008 Chin. Phys. B 17 503
[25]	Wu X J and Wang X Y 2006 Acta Phys. Sin. 55 6261 (in Chinese)

[1]	Circuit realization of the fractional-order unified chaotic system Chen Xiang-Rong(陈向荣), Liu Chong-Xin(刘崇新), and Wang Fa-Qiang(王发强). Chin. Phys. B, 2008, 17(5): 1664-1669.
[2]	Adaptive synchronization of uncertain Liu system via nonlinear input Hu Jia(胡佳) and Zhang Qun-Jiao(张群娇) . Chin. Phys. B, 2008, 17(2): 503-506.
[3]	Chaotic synchronization via linear controller Chen Feng-Xiang(陈凤祥) and Zhang Wei-Dong(张卫东). Chin. Phys. B, 2007, 16(4): 937-941.

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A new kind of nonlinear phenomenon in coupled fractional-order chaotic systems: coexistence of anti-phase and complete synchronization

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