Synchronization between fractional-order chaotic systems and integer orders chaotic systems (fractional-order chaotic systems)

doi:10.1088/1674-1056/19/9/090503

中国物理B ›› 2010, Vol. 19 ›› Issue (9): 90503-090503.doi: 10.1088/1674-1056/19/9/090503

Synchronization between fractional-order chaotic systems and integer orders chaotic systems (fractional-order chaotic systems)

程元明¹, 邝菲¹, 周平²

(1)Institute of Applied Physics, Chongqing University of Posts and Telecommunications, Chongqing 400065, China; (2)Key Laboratory of Network Control and Intelligent Instrument of Ministry of Education, Chongqing University of Posts and Telecommunications, Chongqing 400065, China

收稿日期:2009-12-30 修回日期:2010-02-21 出版日期:2010-09-15 发布日期:2010-09-15
基金资助:
Project supported by the Education Committee of Chongqing Province, China (Grant No. KJ090503).

Synchronization between fractional-order chaotic systems and integer orders chaotic systems (fractional-order chaotic systems)

Zhou Ping(周平)^a)b)†, Cheng Yuan-Ming(程元明)^b), and Kuang Fei(邝菲)^b)

^a Key Laboratory of Network Control and Intelligent Instrument of Ministry of Education, Chongqing University of Posts and Telecommunications, Chongqing 400065, China; ^b Institute of Applied Physics, Chongqing University of Posts and Telecommunications, Chongqing 400065, China

Received:2009-12-30 Revised:2010-02-21 Online:2010-09-15 Published:2010-09-15
Supported by:
Project supported by the Education Committee of Chongqing Province, China (Grant No. KJ090503).

摘要/Abstract

摘要： Based on the idea of tracking control and stability theory of fractional-order systems, a controller is designed to synchronize the fractional-order chaotic system with chaotic systems of integer orders, and synchronize the different fractional-order chaotic systems. The proposed synchronization approach in this paper shows that the synchronization between fractional-order chaotic systems and chaotic systems of integer orders can be achieved, and the synchronization between different fractional-order chaotic systems can also be realized. Numerical experiments show that the present method works very well.

Abstract: Based on the idea of tracking control and stability theory of fractional-order systems, a controller is designed to synchronize the fractional-order chaotic system with chaotic systems of integer orders, and synchronize the different fractional-order chaotic systems. The proposed synchronization approach in this paper shows that the synchronization between fractional-order chaotic systems and chaotic systems of integer orders can be achieved, and the synchronization between different fractional-order chaotic systems can also be realized. Numerical experiments show that the present method works very well.

Key words: fractional-order chaotic systems, chaotic systems of integer orders, different fractional-order chaotic systems, synchronization

中图分类号:

0545

周平, 程元明, 邝菲. Synchronization between fractional-order chaotic systems and integer orders chaotic systems (fractional-order chaotic systems)[J]. 中国物理B, 2010, 19(9): 90503-090503.

Zhou Ping(周平), Cheng Yuan-Ming(程元明), and Kuang Fei(邝菲). Synchronization between fractional-order chaotic systems and integer orders chaotic systems (fractional-order chaotic systems)[J]. Chin. Phys. B, 2010, 19(9): 90503-090503.

参考文献 33

[1]	Ott E, Grebogi C and Yorke J A 1990 Phys. Rev. Lett. 64 1196
[2]	Zhang H G, Liu D R and Wang Z L 2009 Controlling Chaos: Suppression, Synchronization and Chaotizcation (London: Springer Verlag)
[3]	Ma T D, Zhang H G and Fu J 2009 Dynamics of Continuous, Discrete and Impulsive Systems Series B: Applications & Algorithms 16 215
[4]	Zhang H G, Ma T D, Fu J and Tong S C 2009 Chin. Phys. B 18 3751
[5]	Kocarev L and Parlitz U 1995 Phys. Rev. Lett. 74 5208
[6]	Murali K and Lakshmanan M 1998 Phys. Lett. A 241 303
[7]	Zhou P 2007 Chin. Phys. 16 1263
[8]	Ahmad W M and Sprott J C 2003 Chaos, Solitons and Fractals 16 339
[9]	Tikhonov D A and Malchow H 2003 Chaos, Soliton and Fractals 16 287
[10]	Wang F Q and Liu C X 2006 Acta Phys. Sin. 8 3922 (in Chinese)
[11]	Wang X Y, He Y J and Wang M J 2009 Nonlinear Analysis Series A: Theory, Methods & Applications 71 6126
[12]	Mohammad S T and Mohammad H 2007 Phys. Lett. A 367 102
[13]	Mohammad S T and Mohammad H 2008 Physica A 387 57
[14]	Yu Y G and Li H X 2008 Physica A 387 1393
[15]	Li C G and Chen G R 2004 Chaos, Solitons and Fractals 22 549
[16]	Li C P and Peng G J 2004 Chaos, Solitons and Fractals 22 443
[17]	Grigorenko I and Grigorenko E 2003 Phys. Rev. Lett. 91 034101
[18]	Ge Z M and Ou C Y 2007 Chaos, Solitons and Fractals 34 262
[19]	Li C G and Chen G R 2004 Physica A 341 55
[20]	Li C G, Liao X and Yu J B 2003 Phys. Rev. E 68 067203
[21]	Zhou T S and Li C P 2005 Physica D 212 111
[22]	Li C P, Deng W H and Xu D L 2006 Physica A 360 171
[23]	Wang J W, Xiong X H and Zhang Y 2006 Physica A 370 279
[24]	Yan J P and Li C P 2007 Chaos, Solitons and Fractals 32 725
[25]	Li C P and Yan J P 2007 Chaos, Solitons and Fractals 32 751
[26]	Peng G J and Jiang Y L 2008 Phys. Lett. A 372 3963
[27]	Peng G J, Jiang Y L and Chen F 2008 Physica A 387 3738
[28]	Wang X Y and He Y J 2008 Phys. Lett. A 372 435
[29]	Wang X Y and Song J M 2009 Commun. Nonlinear Sci. Numer. Simulat. 14 3351
[30]	Matignon D 1996 IMACS, IEEE-SMC, Lille, France p963
[31]	Chen G and Ueta T 1999 Int. J. Bifur. Chaos 9 1465
[32]	L"u J, Chen G and Zhang S 2002 Int. J. Bifur. Chaos 12 659
[33]	Sheu L J, Chen H K, Chen J H and Tam L M 2007 Chaos, Solitons and Fractals 31 1203 endfootnotesize

Synchronization between fractional-order chaotic systems and integer orders chaotic systems (fractional-order chaotic systems)

Synchronization between fractional-order chaotic systems and integer orders chaotic systems (fractional-order chaotic systems)

PDF (PC)

赞

可视化

摘要/Abstract

引用本文

使用本文

参考文献 33

相关文章 15

Metrics

本文评价

推荐阅读 0

[1]	王兴元, 张娜. Generalised synchronisation of spatiotemporal chaos using feedback control method and phase compression[J]. 中国物理B, 2010, 19(9): 90504-090504.
[2]	王福来. A universal algorithm to generate pseudo-random numbers based on uniform mapping as homeomorphism[J]. 中国物理B, 2010, 19(9): 90505-090505.
[3]	刘兆冰, 张化光, 孙秋野. Novel pinning control strategies for synchronisation of complex networks with nonlinear coupling dynamics[J]. 中国物理B, 2010, 19(9): 90506-090506.
[4]	张晓明, 陈菊芳, 彭建华. Theoretical and experimental study of Chen chaotic system with notch filter feedback control[J]. 中国物理B, 2010, 19(9): 90507-090507.
[5]	周茜, 陈增强. Low dimensional chaos in the AT and GC skew profiles of DNA sequences[J]. 中国物理B, 2010, 19(9): 90508-090508.
[6]	闫华, 魏平, 肖先赐. Tangent response in coupled dynamical systems[J]. 中国物理B, 2010, 19(9): 90501-090501.
[7]	马铁东, 浮洁, 孙跃. An improved impulsive control approach to robust lag synchronization between two different chaotic systems[J]. 中国物理B, 2010, 19(9): 90502-090502.
[8]	Lu Jun-Guo. Another anticontrol method of chaos in the sense of Devaney from a Takagi–Sugeno fuzzy system via the overflow nonlinearity[J]. 中国物理B, 2005, 14(6): 1082-1087.
[9]	窦春霞, 张淑清. H_∞ tracking control of coupled spatiotemporal chaos with parametric uncertainties based on fuzzy observers　　　　　　[J]. 中国物理B, 2005, 14(5): 902-907.
[10]	高心, 虞厥邦. Chaos and chaotic control in a fractional-order electronic oscillator　　　　　[J]. 中国物理B, 2005, 14(5): 908-913.
[11]	禹东川, 吴爱国, 杨朝萍. A novel sliding mode nonlinear proportional-integral control scheme for controlling chaos　　　[J]. 中国物理B, 2005, 14(5): 914-921.
[12]	崔万照, 朱长纯, 保文星, 刘君华. Chaotic time series prediction using mean-field theory for support vector machine　　　　[J]. 中国物理B, 2005, 14(5): 922-929.
[13]	朱加民, 马正义. An extended Jacobian elliptic function method for the discrete mKdV lattice[J]. 中国物理B, 2005, 14(1): 17-20.
[14]	张家树, 李恒超, 肖先赐. Local discrete cosine transformation domain Volterra prediction of chaotic time series[J]. 中国物理B, 2005, 14(1): 49-54.
[15]	王世红, 刘维清, 马宝军, 肖井华, 蒋达娅. Phase synchronization of Chua circuit induced by the periodic signals[J]. 中国物理B, 2005, 14(1): 55-60.