Please wait a minute...
Chin. Phys. B, 2014, Vol. 23(4): 040502    DOI: 10.1088/1674-1056/23/4/040502
GENERAL Prev   Next  

Function projective lag synchronization of fractional-order chaotic systems

Wang Sha (王莎)a, Yu Yong-Guang (于永光)a, Wang Hu (王虎)a, Ahmed Rahmanib
a Department of Mathematics, Beijing Jiaotong University, Beijing 100044, China;
b LAGIS UMR 8219 CNRS, Ecole Centrale de Lille, 59651 Villeneuve d'Ascq, France
Abstract  Function projective lag synchronization of different structural fractional-order chaotic systems is investigated. It is shown that the slave system can be synchronized with the past states of the driver up to a scaling function matrix. According to the stability theorem of linear fractional-order systems, a nonlinear fractional-order controller is designed for the synchronization of systems with the same and different dimensions. Especially, for two different dimensional systems, the synchronization is achieved in both reduced and increased dimensions. Three kinds of numerical examples are presented to illustrate the effectiveness of the scheme.
Keywords:  fractional order      chaos      function projective lag synchronization  
Received:  29 March 2013      Revised:  23 May 2013      Accepted manuscript online: 
PACS:  05.45.Xt (Synchronization; coupled oscillators)  
  05.45.Gg (Control of chaos, applications of chaos)  
Fund: Project supported by the National Natural Science Foundation of China (Grant No. 11371049) and the Science Foundation of Beijing Jiaotong University (Grant Nos. 2011JBM130 and 2011YJS076).
Corresponding Authors:  Wang Sha     E-mail:  saya1016@yahoo.cn
About author:  05.45.Xt; 05.45.Gg

Cite this article: 

Wang Sha (王莎), Yu Yong-Guang (于永光), Wang Hu (王虎), Ahmed Rahmani Function projective lag synchronization of fractional-order chaotic systems 2014 Chin. Phys. B 23 040502

[1] Pecora L M and Carroll T L 1990 Phys. Rev. Lett. 64 821
[2] Pecora L M and Carroll T L 1991 Phys. Rev. A 44 2374
[3] Chen G and Dong X 1998 From Chaos to Order: Methodologies, Perspectives and Applications (Singapore: World Scientific)
[4] Yu H T, Wang J, Deng B, Wei X L and Chen Y Y 2013 Chin. Phys. B 22 058701
[5] Huang J J, Li C D, Zhang W and Wei P C 2012 Chin. Phys. B 21 090508
[6] Lu J F 2008 Commun. Nonlinear Sci. Numer. Simul. 13 1851
[7] Fu J, Yu M and Ma T D 2011 Chin. Phys. B 20 120508
[8] Mahmoud G M and Mahmoud E E 2012 Nonlinear Dyn. 67 1613
[9] Wang G, Shen Y and Yin Q 2013 Chin. Phys. B 22 050504
[10] Tang R A, Liu Y L and Xue J K 2009 Phys. Lett. A 373 1449
[11] Botmart T, Niamsup P and Liu X 2012 Commun. Nonlinear Sci. Numer. Simul. 17 1894
[12] Yu Y G and Li H X 2011 Nonlinear Anal. RWA 12 388
[13] Jawaada W, Noorani M S M and Al-sawalha M M 2012 Chin. Phys. Lett. 29 120505
[14] Podlubny I 1999 Fractional Differential Equations (New York: Academic Press)
[15] Samko S G, Kilbas A A and Marichev Q I 1993 Fractional Integrals and Derivatives: Theory and Applications (New York: Gordon and Breach)
[16] Hilfer R 2001 Applications of Fractional Calculus in Physics (New Jersey: World Scientific)
[17] Han Q, Liu C X, Sun L and Zhu D R 2013 Chin. Phys. B 22 020502
[18] Das S 2007 Functional Fractional Calculus for System Identification and Controls (New York: Springer Berlin Heidelberg)
[19] Tien D N 2013 J. Math. Anal. Appl. 345 702
[20] Kiani-B A, Fallahi K, Pariz N and Leung H 2009 Commun. Nonlinear Sci. Numer. Simul. 14 863
[21] Matignon D 1996 Stability Results of Fractional Differential Equations with Applications to Control Processing (France: IMACS, IEEE-SMC)
[22] Li R H and Chen W S 2013 Chin. Phys. B 22 040503
[23] Mohammad S T and Mohammad H 2008 Physica A 387 57
[24] Zhou P and Zhu W 2011 Nonlinear Anal. RWA 12 811
[25] Yuan L G and Yang Q G 2012 Commun. Nonlinear Sci. Numer. Simul. 17 305
[26] Si G Q, Sun Z Y, Zhang Y B and Chen W Q 2012 Nonlinear Anal. RWA 13 1761
[27] Aghababa M P 2012 Commun. Nonlinear Sci. Numer. Simul. 17 2670
[28] Wang X Y and Zhang H 2013 Chin. Phys. B 22 048902
[29] Ma S Q, Lu Q S and Feng Z S 2010 Int. J. Nonlinear Mech. 45 659
[30] Guo W L 2011 Nonlinear Anal. RWA 12 2579
[31] Li C D, Liao X F and Wong K W 2005 Chaos, Solitons and Fractals 23 183
[32] Li G H 2009 Chaos, Solitons and Fractals 41 2630
[33] Tae H L and Ju H P 2009 Chin. Phys. Lett. 26 090507
[34] Zhang R X and Yang S P 2011 Chin. Phys. B 20 090512
[35] Chen L P, Chai Y and Wu R C 2011 Phys. Lett. A 375 2099
[36] Terman D, Kopell N and Bose A 1998 Physica D 117 241
[37] Dai H, Jia L X and Zhang Y B 2012 Chin. Phys. B 21 120508
[38] Hu M F, Xu Z Y, Zhang R and Hu A H 2007 Phys. Lett. A 365 315
[39] Wang S, Yu Y G and Diao M 2010 Physica A 389 4981
[40] Diethelm K, Ford N J and Freed A D 2002 Nonlinear Dyn. 29 3
[41] Diethelm K, Ford N J and Freed A D 2004 Numer. Algorithms 36 31
[42] Li C G and Chen G R 2004 Physica A 341 55
[43] Mohammad S T and Mohammad H 2007 Phys. Lett. A 367 102
[44] Wang X Y and Song J M 2009 Commun. Nonlinear Sci. Numer. Simul. 14 3351
[45] Hegazi A S and Matouk A E 2011 Appl. Math. Lett. 24 1938
[1] An incommensurate fractional discrete macroeconomic system: Bifurcation, chaos, and complexity
Abderrahmane Abbes, Adel Ouannas, and Nabil Shawagfeh. Chin. Phys. B, 2023, 32(3): 030203.
[2] Memristor hyperchaos in a generalized Kolmogorov-type system with extreme multistability
Xiaodong Jiao(焦晓东), Mingfeng Yuan(袁明峰), Jin Tao(陶金), Hao Sun(孙昊), Qinglin Sun(孙青林), and Zengqiang Chen(陈增强). Chin. Phys. B, 2023, 32(1): 010507.
[3] A novel algorithm to analyze the dynamics of digital chaotic maps in finite-precision domain
Chunlei Fan(范春雷) and Qun Ding(丁群). Chin. Phys. B, 2023, 32(1): 010501.
[4] Synchronously scrambled diffuse image encryption method based on a new cosine chaotic map
Xiaopeng Yan(闫晓鹏), Xingyuan Wang(王兴元), and Yongjin Xian(咸永锦). Chin. Phys. B, 2022, 31(8): 080504.
[5] Multi-target ranging using an optical reservoir computing approach in the laterally coupled semiconductor lasers with self-feedback
Dong-Zhou Zhong(钟东洲), Zhe Xu(徐喆), Ya-Lan Hu(胡亚兰), Ke-Ke Zhao(赵可可), Jin-Bo Zhang(张金波),Peng Hou(侯鹏), Wan-An Deng(邓万安), and Jiang-Tao Xi(习江涛). Chin. Phys. B, 2022, 31(7): 074205.
[6] Bifurcation and dynamics in double-delayed Chua circuits with periodic perturbation
Wenjie Yang(杨文杰). Chin. Phys. B, 2022, 31(2): 020201.
[7] Complex dynamic behaviors in hyperbolic-type memristor-based cellular neural network
Ai-Xue Qi(齐爱学), Bin-Da Zhu(朱斌达), and Guang-Yi Wang(王光义). Chin. Phys. B, 2022, 31(2): 020502.
[8] Energy spreading, equipartition, and chaos in lattices with non-central forces
Arnold Ngapasare, Georgios Theocharis, Olivier Richoux, Vassos Achilleos, and Charalampos Skokos. Chin. Phys. B, 2022, 31(2): 020506.
[9] Resonance and antiresonance characteristics in linearly delayed Maryland model
Hsinchen Yu(于心澄), Dong Bai(柏栋), Peishan He(何佩珊), Xiaoping Zhang(张小平), Zhongzhou Ren(任中洲), and Qiang Zheng(郑强). Chin. Phys. B, 2022, 31(12): 120502.
[10] Finite-time complex projective synchronization of fractional-order complex-valued uncertain multi-link network and its image encryption application
Yong-Bing Hu(胡永兵), Xiao-Min Yang(杨晓敏), Da-Wei Ding(丁大为), and Zong-Li Yang(杨宗立). Chin. Phys. B, 2022, 31(11): 110501.
[11] An image encryption algorithm based on spatiotemporal chaos and middle order traversal of a binary tree
Yining Su(苏怡宁), Xingyuan Wang(王兴元), and Shujuan Lin(林淑娟). Chin. Phys. B, 2022, 31(11): 110503.
[12] Nonlinear dynamics analysis of cluster-shaped conservative flows generated from a generalized thermostatted system
Yue Li(李月), Zengqiang Chen(陈增强), Zenghui Wang(王增会), and Shijian Cang(仓诗建). Chin. Phys. B, 2022, 31(1): 010501.
[13] Control of chaos in Frenkel-Kontorova model using reinforcement learning
You-Ming Lei(雷佑铭) and Yan-Yan Han(韩彦彦). Chin. Phys. B, 2021, 30(5): 050503.
[14] Dynamics analysis in a tumor-immune system with chemotherapy
Hai-Ying Liu(刘海英), Hong-Li Yang(杨红丽), and Lian-Gui Yang(杨联贵). Chin. Phys. B, 2021, 30(5): 058201.
[15] Resistance fluctuations in superconducting KxFe2-ySe2 single crystals studied by low-frequency noise spectroscopy
Hai Zi(子海), Yuan Yao(姚湲), Ming-Chong He(何明冲), Di Ke(可迪), Hong-Xing Zhan(詹红星), Yu-Qing Zhao(赵宇清), Hai-Hu Wen(闻海虎), and Cong Ren(任聪). Chin. Phys. B, 2021, 30(4): 047402.
No Suggested Reading articles found!