Please wait a minute...
Chin. Phys. B, 2010, Vol. 19(11): 110509    DOI: 10.1088/1674-1056/19/11/110509
GENERAL Prev   Next  

Nonlinear feedback synchronisation control between fractional-order and integer-order chaotic systems

Jia Li-Xin(贾立新), Dai Hao(戴浩), and Hui Meng(惠萌)
State Key Laboratory of Electrical Insulation and Power Equipment, School of Electrical Engineering, Xi'an Jiaotong University, Xi'an 710049, China
Abstract  This paper focuses on the synchronisation between fractional-order and integer-order chaotic systems. Based on Lyapunov stability theory and numerical differentiation, a nonlinear feedback controller is obtained to achieve the synchronisation between fractional-order and integer-order chaotic systems. Numerical simulation results are presented to illustrate the effectiveness of this method.
Keywords:  chaos synchronisation      fractional-order chaotic system      nonlinear feedback control      numerical differentiation  
Received:  27 January 2010      Revised:  04 June 2010      Accepted manuscript online: 
PACS:  02.60.Jh (Numerical differentiation and integration)  
  05.45.Gg (Control of chaos, applications of chaos)  
  05.45.Xt (Synchronization; coupled oscillators)  

Cite this article: 

Jia Li-Xin(贾立新), Dai Hao(戴浩), and Hui Meng(惠萌) Nonlinear feedback synchronisation control between fractional-order and integer-order chaotic systems 2010 Chin. Phys. B 19 110509

[1] Dadas S and Momeni H R 2009 Chaos, Solitons and Fractals 42 3140
[2] Pecora L M and Carroll T L 1990 Phys. Rev. Lett. 64 821
[3] Chen F X and Zhang W D 2007 Chin. Phys. 16 937
[4] Li J F, Li N, Liu Y P and Gan Y 2009 Acta Phys. Sin. 58 779 (in Chinese)
[5] Wang X Y and Meng J 2008 Acta Phys. Sin. 57 726 (in Chinese)
[6] Chen M and Han Z 2003 Chaos, Solitons and Fractals 17 709
[7] Ott E F, Grebogi C and Yorke J A 1990 Phys. Rev. Lett. 64 1196
[8] Li W L and Song Y Z 2008 Phys. Rev. Lett. 57 51
[9] Cai G L, Zheng S and Tian L X 2008 Chin. Phys. B 17 2412
[10] Zhang R X, Yang Y and Yang S P 2009 Acta Phys. Sin. 58 6039 (in Chinese)
[11] Kuntanapreeda S 2009 Phys. Lett. A 373 2837
[12] Lorenz E N 1963 J. Atmos. Sci. 20 131
[13] L"u J H and Chen G R 2002 Int. J. Bifurc. Chaos 12 659
[14] Liu C X, Liu T, Liu L and Liu K 2004 Chaos, Solitons and Fractals 22 1031
[15] Hartley T T, Lorenzo C F and Qammer H K 1995 IEEE 42 485
[16] Zhu H, Zhou S B and He Z S 2009 Chaos, Solitons and Fractals 41 2733
[17] Zhang R X and Yang S P 2008 Acta Phys. Sin. 57 6852 (in Chinese)
[18] Wu X J, Li J and Chen G R 2008 Journal of the Franklin Institute 345 392
[19] Hu J and Zhang Q J 2008 Chin. Phys. B 17 503
[20] Gao M and Cui B T 2009 Chin. Phys. B 18 76
[21] Min F H and Wang Z Q 2007 Acta Phys. Sin. 56 6238 (in Chinese)
[22] Deng W H and Li C P 2005 Physica A 353 61
[23] Wang F Q and Liu C X 2006 Acta Phys. Sin. 55 3922 (in Chinese)
[24] Ahmad W M and Sprott J C 2003 Chaos, Solitons and Fractals 16 339 endfootnotesize
[1] Solutions and memory effect of fractional-order chaotic system: A review
Shaobo He(贺少波), Huihai Wang(王会海), and Kehui Sun(孙克辉). Chin. Phys. B, 2022, 31(6): 060501.
[2] A new algorithm for reconstructing the three-dimensional flow field of the oceanic mesoscale eddy
Chao Yan(颜超), Jing Feng(冯径), Ping-Lv Yang(杨平吕), and Si-Xun Huang(黄思训). Chin. Phys. B, 2021, 30(12): 120204.
[3] Topological horseshoe analysis and field-programmable gate array implementation of a fractional-order four-wing chaotic attractor
En-Zeng Dong(董恩增), Zhen Wang(王震), Xiao Yu(于晓), Zeng-Qiang Chen(陈增强), Zeng-Hui Wang(王增会). Chin. Phys. B, 2018, 27(1): 010503.
[4] Prescribed performance synchronization for fractional-order chaotic systems
Liu Heng (刘恒), Li Sheng-Gang (李生刚), Sun Ye-Guo (孙业国), Wang Hong-Xing (王宏兴). Chin. Phys. B, 2015, 24(9): 090505.
[5] Robust sliding mode control for fractional-order chaotic economical system with parameter uncertainty and external disturbance
Zhou Ke (周柯), Wang Zhi-Hui (王智慧), Gao Li-Ke (高立克), Sun Yue (孙跃), Ma Tie-Dong (马铁东). Chin. Phys. B, 2015, 24(3): 030504.
[6] Control of fractional chaotic and hyperchaotic systems based on a fractional order controller
Li Tian-Zeng (李天增), Wang Yu (王瑜), Luo Mao-Kang (罗懋康). Chin. Phys. B, 2014, 23(8): 080501.
[7] Synchronization of uncertain fractional-order chaotic systems with disturbance based on fractional terminal sliding mode controller
Wang Dong-Feng (王东风), Zhang Jin-Ying (张金营), Wang Xiao-Yan (王晓燕). Chin. Phys. B, 2013, 22(4): 040507.
[8] Robust modified projective synchronization of fractional-order chaotic systems with parameters perturbation and external disturbance
Wang Dong-Feng (王东风), Zhang Jin-Ying (张金营), Wang Xiao-Yan (王晓燕). Chin. Phys. B, 2013, 22(10): 100504.
[9] A single adaptive controller with one variable for synchronization of fractional-order chaotic systems
Zhang Ruo-Xun (张若洵), Yang Shi-Ping (杨世平). Chin. Phys. B, 2012, 21(8): 080505.
[10] Modified adaptive controller for synchronization of incommensurate fractional-order chaotic systems
Zhang Ruo-Xun(张若洵) and Yang Shi-Ping(杨世平) . Chin. Phys. B, 2012, 21(3): 030505.
[11] 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). Chin. Phys. B, 2011, 20(8): 080505.
[12] Adaptive stabilization of an incommensurate fractional order chaotic system via a single state controller
Zhang Ruo-Xun(张若洵) and Yang Shi-Ping (杨世平) . Chin. Phys. B, 2011, 20(11): 110506.
[13] Synchronization between fractional-order chaotic systems and integer orders chaotic systems (fractional-order chaotic systems)
Zhou Ping(周平), Cheng Yuan-Ming(程元明), and Kuang Fei(邝菲). Chin. Phys. B, 2010, 19(9): 090503.
[14] A specific state variable for a class of 3D continuous fractional-order chaotic systems
Zhou Ping(周平), Cheng Yuan-Ming(程元明), and Kuang Fei(邝菲). Chin. Phys. B, 2010, 19(7): 070507.
[15] Nonlinear feedback control of a novel hyperchaotic system and its circuit implementation
Wang Hao-Xiang(汪浩祥), Cai Guo-Liang(蔡国梁), Miao Sheng(缪盛), and Tian Li-Xin(田立新). Chin. Phys. B, 2010, 19(3): 030509.
No Suggested Reading articles found!