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Chin. Phys. B, 2011, Vol. 20(6): 060505    DOI: 10.1088/1674-1056/20/6/060505
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The synchronization of a fractional order hyperchaotic system based on passive control

Wu Chao-Jun(吴朝俊)a)b)† , Zhang Yan-Bin(张彦斌)a)b), and Yang Ning-Ning(杨宁宁) a)b)
State Key Laboratory of Electrical Insulation and Power Equipment, Xi'an 710049, China; School of Electrical Engineering, Xi'an Jiaotong University, Xi'an 710049, China
Abstract  This paper investigates the synchronization of a fractional order hyperchaotic system using passive control. A passive controller is designed, based on the properties of a passive system. Then the synchronization between two fractional order hyperchaotic systems under different initial conditions is realized, on the basis of the stability theorem for fractional order systems. Numerical simulations and circuitry simulations are presented to verify the analytical results.
Keywords:  fractional order hyperchaos      passive control      numerical simulation      circuitry simulation  
Received:  23 November 2010      Revised:  16 January 2011      Accepted manuscript online: 
PACS:  05.45.Xt (Synchronization; coupled oscillators)  
  05.45.Pq (Numerical simulations of chaotic systems)  

Cite this article: 

Wu Chao-Jun(吴朝俊), Zhang Yan-Bin(张彦斌), and Yang Ning-Ning(杨宁宁) The synchronization of a fractional order hyperchaotic system based on passive control 2011 Chin. Phys. B 20 060505

[1] Hartley T T, Lorenzo C F and Qammer H K 1995 IEEE Trans. CAS-I 42 485
[2] Wu Z M, Lu J G and Xie J Y 2006 Chin. Phys. 15 1201
[3] Li C G and Chen G 2004 Physica A 341 55
[4] Ahmad W M and Sprott J C 2003 Chaos, Solitons and Fractals 16 339
[5] Ahmad W M and Harb W M 2003 Chaos, Solitons and Fractals 18 693
[6] Li C P and Peng G J 2004 Chaos, Solitons and Fractals 22 443
[7] Lu J G and Chen G R 2006 Chaos, Solitons and Fractals 27 685
[8] Tavazoei M S and Haeri M 2007 Phys. Lett. A 367 102
[9] Liu L, Liu C X and Zhang Y B 2009 Int. J. Bifurc. Chaos 19 2473
[10] Yu Y G and Li H X 2008 Physica A 387 1393
[11] Lu J J and Liu C X 2007 Chin. Phys. 16 1586
[12] Pecora L M and Carroll T L 1990 Phys. Rev. Lett. 64 821
[13] Liu F, Ren Y, Shan X M and Qiu Z L 2002 Chaos, Solitons and Fractals 13 723
[14] Li G H 2005 Chin. Phys. 14 472
[15] Zhang H, Ma X K, Yang Y and Xu C D 2005 Chin. Phys. 14 86
[16] Feng J W, Chen S H and Wang C P 2005 Chaos, Solitons and Fractals 26 1163
[17] Wang Y W, Guan Z H and Xiao J W 2004 Chaos 14 200
[18] Ma T D, Zhang H G and Fu J 2009 Dynamics of Continuous, Discrete and Impulsive Systems Series B: Applications & Algorithms 16 215
[19] Yang N N, Liu C X and Wu C J 2010 Chin. Phys. B 19 100502
[20] Li M and Liu C X 2010 Chin. Phys. B 19 100504
[21] Ma T D, Zhang H G and Fu J 2008 Chin. Phys. B 17 4407
[22] Zhou P, Wei L J and Cheng X F 2009 Chin. Phys. B 18 2674
[23] Varsha Daftardar Gejji and Sachin Bhalekar 2010 Comput. Math. Appl. 59 1117
[24] Wu X J, Lu H T and Shen S L 2009 Phys. Lett. A 373 2329
[25] Wen Y 1999 IEEE Trans. CAS-I 46 876
[26] Wang F Q and Liu C X 2007 Physica D: Nonlinear Phenomena 225 50
[27] Byrnes C I, Isidori A and Willems J C 1991 IEEE Trans. Auto. Control 36 1228
[28] Lin W 1997 Automatica 33 453
[29] Liu C X 2007 The Theory and Application of Nonlinear Circuits (Xián: Xián Jiaotong University Press) p. 250 (in Chinese)
[30] Charef A, Sun H H, Tsao Y Y and Onaral B 1992 IEEE Trans. Automat. Control 37 1465
[31] Wang F Q and Liu C X 2006 Chin. Phys. 15 1971
[32] Wei D Q and Luo X S 2008 Chin. Phys. B 17 92
[33] Hu J B, Han Y and Zhao L D 2009 Acta Phys. Sin. 58 4402 (in Chinese)
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