A general method for synchronizing an integer-order chaotic system and a fractional-order chaotic system

doi:10.1088/1674-1056/20/8/080505

Abstract This paper investigates the synchronization between integer-order and fractional-order chaotic systems. By introducing fractional-order operators into the controllers, the addressed problem is transformed into a synchronization one among integer-order systems. A novel general method is presented in the paper with rigorous proof. Based on this method, effective controllers are designed for the synchronization between Lorenz systems with an integer order and a fractional order, and for the synchronization between an integer-order Chen system and a fractional-order Liu system. Numerical results, which agree well with the theoretical analyses, are also given to show the effectiveness of this method.

Keywords: chaos synchronization integer-order chaotic system fractional-order chaotic system fractional calculus

Received: 19 January 2011
Revised: 13 March 2011
Accepted manuscript online:

PACS:	05.45.Pq	(Numerical simulations of chaotic systems)
	05.45.Xt	(Synchronization; coupled oscillators)
	05.45.Gg	(Control of chaos, applications of chaos)

Cite this article:

Si Gang-Quan(司刚全), Sun Zhi-Yong(孙志勇), and Zhang Yan-Bin(张彦斌) A general method for synchronizing an integer-order chaotic system and a fractional-order chaotic system 2011 Chin. Phys. B 20 080505

[1]	Diethelm K 2010 The Analysis of Fractional Differential Equations (Berlin: Springer)
[2]	Grigorenko I and Grigorenko E 2003 Phys. Rev. Lett. 91 34101
[3]	Li C and Chen G 2004 Physica A 341 55
[4]	Li C and Chen G 2004 Chaos, Solitons & Fractals 22 549
[5]	Lu J J and Liu C X 2007 Chin. Phys. 16 1586
[6]	Boccaletti S, Kurths J, Osipov G, Valladares D and Zhou C 2002 Phys. Rep. 366 1
[7]	Wu Z M and Xie J Y 2007 Chin. Phys. 16 1901
[8]	Zhou P, Wei L J and Cheng X F 2009 Chin. Phys. B 18 2674
[9]	Zhang R X and Yang S P 2010 Chin. Phys. B 19 020510
[10]	Wang J W and Chen A M 2010 Chin. Phys. Lett. 27 110501
[11]	Wu D and Li J J 2010 Chin. Phys. B 19 120505
[12]	Zhang R and Xu Z Y 2010 Chin. Phys. B 19 120511
[13]	Lee S M, Kwon O M and Park J H 2011 Chin. Phys. B 20 010506
[14]	Li H Q, Liao X F and Huang H Y 2011 Acta Phys. Sin. 60 020512 (in Chinese)
[15]	Zhou P and Kuang F 2010 Acta Phys. Sin. 59 6851 (in Chinese)
[16]	Zhou P, Cheng Y M and Kuang F 2010 Chin. Phys. B 19 090503
[17]	Zhou P and Cao Y X 2010 Chin. Phys. B 19 100507
[18]	Odibat Z M 2010 Nonlinear Dyn. 60 479
[19]	Jia L X, Dai H and Hui M 2010 Chin. Phys. B 19 110509
[20]	Podlubny I 1999 Fractional Differential Equations (New York: Academic Press)
[21]	Hartley T T, Lorenzo C F and Qammer K 1995 IEEE Trans. Circuits Syst. I 42 485
[22]	Tavazoei M S 2009 IEEE Trans. Circuits Syst. II 56 519
[23]	Vinagre B M, Podlubny I, Hernandez A and Feliu V 2000 Fractional Calculus & Appl. Anal. 3 231
[24]	Oustaloup A, Levron F, Mathieu B and Nanot F 2000 IEEE Trans. Circuits Syst. I 47 25
[25]	Valerio D and Sa da Costa J 2004 Fractional Derivatives and Applications, IFAC, Bordeaux
[26]	Lorenz E N 1963 J. Atmos. Sci. 20 130
[27]	Chen G and Ueta T 1999 Int. J. Bifur. Chaos 9 1465
[28]	Liu C, Liu T, Liu L and Liu K 2004 Chaos, Solitons & Fractals 22 1031
[29]	Xu Z and Liu C X 2008 Chin. Phys. B 17 4033

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A general method for synchronizing an integer-order chaotic system and a fractional-order chaotic system

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