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Based on the idea of tracking control and the stability theory of linear fractional-order system, chaotic synchronization between fractional-order chaotic system and chaotic system of integer orders is proposed. A compensation controller and a feedback controller are given. Synchronization between the fractional-order Chen chaotic system and the Loren chaotic system of integer orders is used to illustrate the effectiveness of the proposed synchronization approach. Numerical and circuit simulations coincide with the theoretical analysis.
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Keywords:
- fractional-order chaotic system /
- chaotic system of integer orders /
- chaotic synchronization /
- tracking control
[1] Pecora L M, Carroll T L 1990 Phys. Rev. Lett. 64 821
[2] Li Z G, Xu D L 2001 Phys. Lett. A 282 175
[3] Lu J Q, Xi Y G 2003 Chaos Soliton Fract. 17 825
[4] Zou Y L, Zhu J 2006 Chin. Phys. 15 1965
[5] Lǔ L, Luan L, Guo Z A 2007 Chin. Phys. 16 346
[6] Liu Y Z, Jiang C S, Lin C S 2007 Acta Phys. Sin. 56 707 (in Chinese)[刘扬正、 姜长圣、 林长圣 2007 物理学报 56 707]
[7] Wang X Y, Meng J 2008 Acta Phys. Sin. 57 726 (in Chinese)[王兴元、 孟 娟 2008 物理学报 57 726]
[8] Gao X, Yu J B 2005 Chin. Phys. 14 908
[9] Grigorenko I, Grigorenko E 2003 Phys. Rev. Lett. 91 034101
[10] Li C G, Chen G 2004 Physica A 341 55
[11] Ahmad W M, Sprott J C 2003 Chaos Soliton Fract. 16 339
[12] Li C G, Liao X F, Yu J B 2003 Phys. Rev. E 68 067203
[13] Zhou P 2007 Chin. Phys. 16 1263
[14] Peng G J, Jiang Y L 2008 Phys. Lett. A 372 3963
[15] Chen X R, Liu C X, Li Y X 2008 Acta Phys. Sin. 57 (in Chinese) 1453[陈向荣、 刘崇新、 李永勋 2008 物理学报 57 1453]
[16] Peng G J, Jiang Y L, Chen F 2008 Physica A 387 3738
[17] Shao S Q 2009 Chaos Soliton. Fract. 39 1572
[18] Zhou P, Wei L J, Cheng X F 2009 Chin. Phys. B 18 2674
[19] Lorenz E N 1963 J. Atmos. Sci. 20 130
[20] Chen G, Ueta T 1999 Int. J. Bifur. Chaos 9 1465
[21] Mohammad S T, Mohammad H 2007 Phys. Lett. A 367 102
[22] Wang X Y, Shi Q J 2005 Acta Phys. Sin. 54 5591 (in Chinese) [王兴元、 石其江 2005 物理学报 54 5591]
[23] Min F H, Wang Z Q 2008 Acta Phys. Sin. 57 31 (in Chinese) [闵富红、 王执铨 2008 物理学报 57 31]
[24] Li C L, Luo X S 2009 Acta Phys. Sin. 58 3759 (in Chinese) [李春来、 罗晓曙 2009 物理学报 58 3759]
[25] Liu J J, Liu C X 2007 Chin. Phys. 16 1586
[26] Wang F Q, Liu C X 2006 Acta Phys. Sin. 55 3922 (in Chinese) [王发强、 刘崇新 2006 物理学报 55 3922]
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[1] Pecora L M, Carroll T L 1990 Phys. Rev. Lett. 64 821
[2] Li Z G, Xu D L 2001 Phys. Lett. A 282 175
[3] Lu J Q, Xi Y G 2003 Chaos Soliton Fract. 17 825
[4] Zou Y L, Zhu J 2006 Chin. Phys. 15 1965
[5] Lǔ L, Luan L, Guo Z A 2007 Chin. Phys. 16 346
[6] Liu Y Z, Jiang C S, Lin C S 2007 Acta Phys. Sin. 56 707 (in Chinese)[刘扬正、 姜长圣、 林长圣 2007 物理学报 56 707]
[7] Wang X Y, Meng J 2008 Acta Phys. Sin. 57 726 (in Chinese)[王兴元、 孟 娟 2008 物理学报 57 726]
[8] Gao X, Yu J B 2005 Chin. Phys. 14 908
[9] Grigorenko I, Grigorenko E 2003 Phys. Rev. Lett. 91 034101
[10] Li C G, Chen G 2004 Physica A 341 55
[11] Ahmad W M, Sprott J C 2003 Chaos Soliton Fract. 16 339
[12] Li C G, Liao X F, Yu J B 2003 Phys. Rev. E 68 067203
[13] Zhou P 2007 Chin. Phys. 16 1263
[14] Peng G J, Jiang Y L 2008 Phys. Lett. A 372 3963
[15] Chen X R, Liu C X, Li Y X 2008 Acta Phys. Sin. 57 (in Chinese) 1453[陈向荣、 刘崇新、 李永勋 2008 物理学报 57 1453]
[16] Peng G J, Jiang Y L, Chen F 2008 Physica A 387 3738
[17] Shao S Q 2009 Chaos Soliton. Fract. 39 1572
[18] Zhou P, Wei L J, Cheng X F 2009 Chin. Phys. B 18 2674
[19] Lorenz E N 1963 J. Atmos. Sci. 20 130
[20] Chen G, Ueta T 1999 Int. J. Bifur. Chaos 9 1465
[21] Mohammad S T, Mohammad H 2007 Phys. Lett. A 367 102
[22] Wang X Y, Shi Q J 2005 Acta Phys. Sin. 54 5591 (in Chinese) [王兴元、 石其江 2005 物理学报 54 5591]
[23] Min F H, Wang Z Q 2008 Acta Phys. Sin. 57 31 (in Chinese) [闵富红、 王执铨 2008 物理学报 57 31]
[24] Li C L, Luo X S 2009 Acta Phys. Sin. 58 3759 (in Chinese) [李春来、 罗晓曙 2009 物理学报 58 3759]
[25] Liu J J, Liu C X 2007 Chin. Phys. 16 1586
[26] Wang F Q, Liu C X 2006 Acta Phys. Sin. 55 3922 (in Chinese) [王发强、 刘崇新 2006 物理学报 55 3922]
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