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There is larger key space in fractional order hyperchaotic systems (FOHS), however, the FOHS with different structures are more common in the field of secret communication. Therefore, it is important to study the synchronization method of the system. In this paper, the synchronization between two different FOHS is investigated. i.e., the Chen FOHS and the Rssler FOHs. Based on the fractional order stability theory, two different controllers are designed for synchronizing the drive system and the response system. When the parameters are known in advance, active control synchronization is adopted, the method is simple without constructing any special function. When the parameters are fully unknown, a adaptive control law and a parameter update rule are introduced. Numerical simulations are presented to verify the effectiveness and the feasibility of the synchronization scheme.
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Keywords:
- the Chen fractional order hyperchaotic system (FOHS) /
- the Rssler FOHS /
- active control synchronization /
- adaptive synchronization
[1] Pecora L M, Carroll T L 1990 Phys. Rev. Lett. 64 821
[2] Bai E W, Lonngren K E 2000 Chaos, Solitons & Fractals 11 1041
[3] Fradkov A L, Pogromsky Y A 1996 IEEE Trans. Circuits & Systems-I 43 907
[4] Andrievsky B 2002 Math. Comp. Simu. 58 289
[5] Cai G L, Huang J J 2007 J. Jiangsu Univ.: Nat. Sci. Ed. 28 269 (in Chinese) [蔡国梁, 黄娟娟 2007 江苏大学学报:自然科学版 28 269]
[6] Gao J F, Luo X J, Ma X K 1999 Acta Phys. Sin. 48 1618 (in Chinese) [高金峰, 罗先觉, 马西奎 1999 48 1618]
[7] Peng C C, Chen C L 2008 Chaos,Solitons & Fractals 37 598
[8] Ahmad M, Ashraf A Z, Ahmad A A 2007 Chaos, Solitons & Fractals 34 639
[9] Tang Y, Fang J A 2010 Commun. Nonlinear Sci. Numer. Simulat. 15 401
[10] Mohammad S T, Mohammad H 2008 Physica A 387 57
[11] Cai G L, Huang J J 2006 Acta Phys. Sin. 55 3997 (in Chinese) [蔡国梁, 黄娟娟 2006 55 3997]
[12] Yu Y G, Wen G G, Li H X 2009 Int. J. Nonlin. Sci. Num. 10 379
[13] Xu C, Wu G, Feng J W 2008 Int. J. Nonlin. Sci. Num. 9 89
[14] Zhou P, Kuang F 2010 Acta Phys. Sin. 59 6851 (in Chinese) [周平, 邝菲 2010 59 6851]
[15] Hu J B, Han Y, Zhao L D 2008 Acta Phys. Sin. 57 7522 (in Chinese) [胡建兵, 韩焱, 赵灵冬 2008 57 7522]
[16] Hu J B, Han Y, Zhao L D 2009 Acta Phys. Sin. 58 2235 ( in Chinese) [胡建兵, 韩焱, 赵灵冬 2009 58 2235]
[17] Zhao L D, Hu J B, Liu X H 2010 Acta Phys. Sin. 59 2305 (in Chinese) [赵灵冬, 胡建兵, 刘旭辉 2010 59 2305]
[18] Yan Z Y 2005 Appl . Math. Comp. 168 1239
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[1] Pecora L M, Carroll T L 1990 Phys. Rev. Lett. 64 821
[2] Bai E W, Lonngren K E 2000 Chaos, Solitons & Fractals 11 1041
[3] Fradkov A L, Pogromsky Y A 1996 IEEE Trans. Circuits & Systems-I 43 907
[4] Andrievsky B 2002 Math. Comp. Simu. 58 289
[5] Cai G L, Huang J J 2007 J. Jiangsu Univ.: Nat. Sci. Ed. 28 269 (in Chinese) [蔡国梁, 黄娟娟 2007 江苏大学学报:自然科学版 28 269]
[6] Gao J F, Luo X J, Ma X K 1999 Acta Phys. Sin. 48 1618 (in Chinese) [高金峰, 罗先觉, 马西奎 1999 48 1618]
[7] Peng C C, Chen C L 2008 Chaos,Solitons & Fractals 37 598
[8] Ahmad M, Ashraf A Z, Ahmad A A 2007 Chaos, Solitons & Fractals 34 639
[9] Tang Y, Fang J A 2010 Commun. Nonlinear Sci. Numer. Simulat. 15 401
[10] Mohammad S T, Mohammad H 2008 Physica A 387 57
[11] Cai G L, Huang J J 2006 Acta Phys. Sin. 55 3997 (in Chinese) [蔡国梁, 黄娟娟 2006 55 3997]
[12] Yu Y G, Wen G G, Li H X 2009 Int. J. Nonlin. Sci. Num. 10 379
[13] Xu C, Wu G, Feng J W 2008 Int. J. Nonlin. Sci. Num. 9 89
[14] Zhou P, Kuang F 2010 Acta Phys. Sin. 59 6851 (in Chinese) [周平, 邝菲 2010 59 6851]
[15] Hu J B, Han Y, Zhao L D 2008 Acta Phys. Sin. 57 7522 (in Chinese) [胡建兵, 韩焱, 赵灵冬 2008 57 7522]
[16] Hu J B, Han Y, Zhao L D 2009 Acta Phys. Sin. 58 2235 ( in Chinese) [胡建兵, 韩焱, 赵灵冬 2009 58 2235]
[17] Zhao L D, Hu J B, Liu X H 2010 Acta Phys. Sin. 59 2305 (in Chinese) [赵灵冬, 胡建兵, 刘旭辉 2010 59 2305]
[18] Yan Z Y 2005 Appl . Math. Comp. 168 1239
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