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Designing a suitable response system to a class of fractional order chaotic systems, we can realize the modification of projective synchronization for these systems by only transmitting a single variable. Since chaos synchronization can be achieved by transmitting the single variable from driving system to response system, this method is more practical. Numerical simulation of fractional order unified chaotic system demonstrates the effectiveness of the proposed method.
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Keywords:
- modified projective synchronization /
- single driving variable /
- fractional-order unified chaotic system
[1] Lorenz E N, 1963 J. Atmas. Sci. 20 131
[2] Chinese)[张成芬、 高金峰、 徐 磊 2007 物理学报 56 5124]
[3] Hartly T T, Lorenz C F, Qammer H K 1995 IEEE Trans. CAS-Ⅰ 42 485
[4] Chen G R,Ueta T 1999 Int. J. Bifuec. Chaos 9 1465
[5] Lü J H, Chen G R,Cheng D,Celikovsky S 2002 Int. J. Bifuec. Chaos 12 2917
[6] Li C G, Chen G R 2004 Physica A 341 55
[7] Liu C X 2007 Acta Phys. Sin. 56 6865 (in Chinese)[刘崇新 2007 物理学报 56 6865]
[8] Zhang R X,Yang Y,Yang S P 2009 Acta Phys. Sin. 58 6039 (in Chinese)[张若洵、 杨 洋、 杨世平 2009 物理学报 58 6039]
[9] Wang X Y,He Y J 2008 Acta Phys. Sin. 57 485 (in Chinese)[王兴元、 贺毅杰 2008 物理学报 57 485]
[10] Zhang C F,Gao J F,Xu L 2007 Acta Phys. Sin. 56 5124 (in
[11] Li G H 2007 Chaos, Solitons and Fractals 32 1786
[12] Park J H 2007 Chaos, Solitons and Fractals 34 1154
[13] Yang T, Fang J A 2008 Physics Letters A 372 1816
[14] Caputo M 1967 The Geophysical Joumal of the Royal Astronomical Society 13 529
[15] Charef A, Sun H H, Tsao Y Y, Onaral B 1992 IEEE Trans. Auto. Contr. 37 9
[16] Li C P, Peng G J 2004 Chaos, Solitons and Fractals 22 443
[17] Matignon D 1996 IMACS-SMC Proceedings (Lille:IEEE) 963
[18] Wu X J, Li J, Chen G R 2008 Journal of the Franklin Institute 345 392
[19] Lü J H, Chen G R 2002 Bifurcation and Chaos 12 659
[20] Lu J, Han F L, Yu X H, Chen G R 2004 Automatica 40 1677
[21] Lü J H, Chen G R 2006 Int. J. Bifurcation and Chaos 16 775
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[1] Lorenz E N, 1963 J. Atmas. Sci. 20 131
[2] Chinese)[张成芬、 高金峰、 徐 磊 2007 物理学报 56 5124]
[3] Hartly T T, Lorenz C F, Qammer H K 1995 IEEE Trans. CAS-Ⅰ 42 485
[4] Chen G R,Ueta T 1999 Int. J. Bifuec. Chaos 9 1465
[5] Lü J H, Chen G R,Cheng D,Celikovsky S 2002 Int. J. Bifuec. Chaos 12 2917
[6] Li C G, Chen G R 2004 Physica A 341 55
[7] Liu C X 2007 Acta Phys. Sin. 56 6865 (in Chinese)[刘崇新 2007 物理学报 56 6865]
[8] Zhang R X,Yang Y,Yang S P 2009 Acta Phys. Sin. 58 6039 (in Chinese)[张若洵、 杨 洋、 杨世平 2009 物理学报 58 6039]
[9] Wang X Y,He Y J 2008 Acta Phys. Sin. 57 485 (in Chinese)[王兴元、 贺毅杰 2008 物理学报 57 485]
[10] Zhang C F,Gao J F,Xu L 2007 Acta Phys. Sin. 56 5124 (in
[11] Li G H 2007 Chaos, Solitons and Fractals 32 1786
[12] Park J H 2007 Chaos, Solitons and Fractals 34 1154
[13] Yang T, Fang J A 2008 Physics Letters A 372 1816
[14] Caputo M 1967 The Geophysical Joumal of the Royal Astronomical Society 13 529
[15] Charef A, Sun H H, Tsao Y Y, Onaral B 1992 IEEE Trans. Auto. Contr. 37 9
[16] Li C P, Peng G J 2004 Chaos, Solitons and Fractals 22 443
[17] Matignon D 1996 IMACS-SMC Proceedings (Lille:IEEE) 963
[18] Wu X J, Li J, Chen G R 2008 Journal of the Franklin Institute 345 392
[19] Lü J H, Chen G R 2002 Bifurcation and Chaos 12 659
[20] Lu J, Han F L, Yu X H, Chen G R 2004 Automatica 40 1677
[21] Lü J H, Chen G R 2006 Int. J. Bifurcation and Chaos 16 775
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