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In this paper, a method of modified function projective synchronization for a class of partially linear fractional order chaotic systems is proposed. This kind of system can be constructed by single variable coupling response system. The modified function projective synchronization controller is designed by Routh-Hurwitz conditions. Theoretical analyses and numerical simulations of two chaotic systems verify the effectiveness of the proposed method.
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Keywords:
- fractional order chaotic systems /
- partially linear /
- modified function projective synchronization
[1] Pecora L M, Carroll T L 1990 Phys. Rev. Lett. 64 821
[2] Liu J G, 2012 Chin. Phys. B 21 120506
[3] Wang X Y, Meng J 2008 Acta Phys. Sin. 57 726 (in Chinese) [王兴元, 孟娟 2008 57 726]
[4] Lu J Q, Cao J D 2005 Chaos 15 043901
[5] Liu J, Chen S H, Lu J A 2003 Acta Phys. Sin. 52 1595 (in Chinese) [刘杰, 陈士华, 陆君安 2003 52 1595]
[6] Sang J Y, Yang J, Yue L J 2011 Chin. Phys. B 20 080507
[7] Wang X Y, He Y 2008 Phys. Rev. A 372 435
[8] Wang X Y, Wang Y 2007 Acta Phys. Sin. 56 2498 (in Chinese) [王兴元, 王勇 2007 56 2498]
[9] Wang X Y, Zhang Y L 2011 Chin. Phys. B 20 100506
[10] Wang X Y, Zhang X P, Ma C 2012 Nonlinear Dyn. 69 511
[11] Yang X K, Cai L, Zhao X H, Feng C W 2010 Acta Phys. Sin. 59 3740 (in Chinese) [杨晓阔, 蔡理, 赵晓辉, 冯朝文 2010 59 3740]
[12] Li J F, Li N 2011 Acta Phys. Sin. 60 080507 (in Chinese) [李建芬, 李农 2011 60 080507]
[13] Deng W, Fang J, Wu Z J, Wu Y M 2012 Acta Phys. Sin. 61 140503 (in Chinese) [邓玮, 方洁, 吴振军, 吴艳敏 2012 61 140503]
[14] Zhou P, Ding R 2012 Indian J. Phys. 86 497
[15] Zhou P, Zhu W 2011 Nonlinear Anal. B: Real World Appl. 12 811
[16] Wang J A, Liu H P 2010 Acta Phys. Sin. 59 2264 (in Chinese) [王健安, 刘贺平 2010 59 2264]
[17] Mainieri R, Rehacek J 1999 Phys. Rev. Lett. 82 3042
[18] Xu D, Li Z G 2002 Int. J. Bifur. Chaos 12 1395
[19] Hu M F, Xu Z Y 2008 Nonlinear Anal. B: Real World Appl. 9 1253
[20] Hu M F, Xu Z Y, Zhang R, Hu A H 2007 Phys. Lett. A 365 315
[21] Matignon D 1996 In Computational Engineering in Systems and Application Multiconference Lille France 2 963
[22] Ahmed E, El-Sayed A M A, Elsaka H A A 2007 J. Math. Anal. Appl. 325 542
[23] Lu J, Zhou T, Zhang S 2002 Chaos Soliton. Fract. 14 529241
[24] Benettin G, Galgani L, Strelcyn J M 1976 Phys. Rev. A 14 2338
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[1] Pecora L M, Carroll T L 1990 Phys. Rev. Lett. 64 821
[2] Liu J G, 2012 Chin. Phys. B 21 120506
[3] Wang X Y, Meng J 2008 Acta Phys. Sin. 57 726 (in Chinese) [王兴元, 孟娟 2008 57 726]
[4] Lu J Q, Cao J D 2005 Chaos 15 043901
[5] Liu J, Chen S H, Lu J A 2003 Acta Phys. Sin. 52 1595 (in Chinese) [刘杰, 陈士华, 陆君安 2003 52 1595]
[6] Sang J Y, Yang J, Yue L J 2011 Chin. Phys. B 20 080507
[7] Wang X Y, He Y 2008 Phys. Rev. A 372 435
[8] Wang X Y, Wang Y 2007 Acta Phys. Sin. 56 2498 (in Chinese) [王兴元, 王勇 2007 56 2498]
[9] Wang X Y, Zhang Y L 2011 Chin. Phys. B 20 100506
[10] Wang X Y, Zhang X P, Ma C 2012 Nonlinear Dyn. 69 511
[11] Yang X K, Cai L, Zhao X H, Feng C W 2010 Acta Phys. Sin. 59 3740 (in Chinese) [杨晓阔, 蔡理, 赵晓辉, 冯朝文 2010 59 3740]
[12] Li J F, Li N 2011 Acta Phys. Sin. 60 080507 (in Chinese) [李建芬, 李农 2011 60 080507]
[13] Deng W, Fang J, Wu Z J, Wu Y M 2012 Acta Phys. Sin. 61 140503 (in Chinese) [邓玮, 方洁, 吴振军, 吴艳敏 2012 61 140503]
[14] Zhou P, Ding R 2012 Indian J. Phys. 86 497
[15] Zhou P, Zhu W 2011 Nonlinear Anal. B: Real World Appl. 12 811
[16] Wang J A, Liu H P 2010 Acta Phys. Sin. 59 2264 (in Chinese) [王健安, 刘贺平 2010 59 2264]
[17] Mainieri R, Rehacek J 1999 Phys. Rev. Lett. 82 3042
[18] Xu D, Li Z G 2002 Int. J. Bifur. Chaos 12 1395
[19] Hu M F, Xu Z Y 2008 Nonlinear Anal. B: Real World Appl. 9 1253
[20] Hu M F, Xu Z Y, Zhang R, Hu A H 2007 Phys. Lett. A 365 315
[21] Matignon D 1996 In Computational Engineering in Systems and Application Multiconference Lille France 2 963
[22] Ahmed E, El-Sayed A M A, Elsaka H A A 2007 J. Math. Anal. Appl. 325 542
[23] Lu J, Zhou T, Zhang S 2002 Chaos Soliton. Fract. 14 529241
[24] Benettin G, Galgani L, Strelcyn J M 1976 Phys. Rev. A 14 2338
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