|
|
A general method for synchronizing an integer-order chaotic system and a fractional-order chaotic system |
Si Gang-Quan(司刚全), Sun Zhi-Yong(孙志勇)†, and Zhang Yan-Bin(张彦斌) |
State Key Laboratory of Electrical Insulation and Power Equipment, School of Electrical Engineering, Xi'an Jiaotong University, Xi'an 710049, China |
|
|
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.
|
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
|
No Suggested Reading articles found! |
|
|
Viewed |
|
|
|
Full text
|
|
|
|
|
Abstract
|
|
|
|
|
Cited |
|
|
|
|
Altmetric
|
blogs
Facebook pages
Wikipedia page
Google+ users
|
Online attention
Altmetric calculates a score based on the online attention an article receives. Each coloured thread in the circle represents a different type of online attention. The number in the centre is the Altmetric score. Social media and mainstream news media are the main sources that calculate the score. Reference managers such as Mendeley are also tracked but do not contribute to the score. Older articles often score higher because they have had more time to get noticed. To account for this, Altmetric has included the context data for other articles of a similar age.
View more on Altmetrics
|
|
|