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In view of chaos synchronization of a class of fractional-order chaotic systems, a novel adaptive controller and adaptive updating law are designed based on the quasi-Lyapunov stability theory for fractional-order systems. The derived method has some advantages such as simple structure, low control cost and high generality compared with the existing results. Furthermore, the method can be applied to most typical fractional-order chaotic systems. Finally, numerical simulations are used to illustrate the effectiveness of the proposed synchronization method.
[1] [2] Gao X, Yu J B 2005 Chin. Phys. 14 908
[3] [4] Lu J G 2006 Physica A 359 107
[5] Yu Y G, Li H X, Wang S 2009 Chaos Soliton. Fract. 42 1181
[6] [7] [8] Li C G, Chen G R 2004 Physica A 341 55
[9] [10] Lu J G 2006 Phys. Lett. A 354 305
[11] [12] Pecora L M, Carroll T L 1990 Phys. Rev. Lett. 64 821
[13] [14] Zhang H G, Ma T D, Huang G B, Wang Z L 2010 IEEE Trans. Syst. Man Cybern. B 40 831
[15] [16] Wang M J, Wang X Y 2011 Int. J. Mod. Phys. B 25 1283
[17] [18] Ma T D, Fu J, Sun Y 2010 Chin. Phys. B 19 090502
[19] [20] Wang X Y, Liu R, Zhang N 2011 Commun. Theor. Phys. 55 617
[21] 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 58 6039]
[22] [23] Chen L P, Chai Y, Wu R C 2011 Phys. Lett. A 375 2099
[24] [25] Wang M J, Wang X Y, Niu Y J 2011 Chin. Phys. B 20 010508
[26] [27] [28] Wang X Y, Zhang Y L, Lin D, Zhang N 2011 Chin. Phys. B 20 030506
[29] Niu Y J, Wang X Y, Nian F Z, Wang M J 2010 Chin. Phys. B 19 120507
[30] [31] [32] Jia L X, Dai H, Hui M 2010 Chin. Phys. B 19 110509
[33] Chen X R, Liu C X, Wang F Q, Li Y X 2008 Acta Phys. Sin. 57 1416 (in Chinese) [陈向荣,刘崇新,王发强,李永勋 2008 57 1416]
[34] [35] Min F H, Yu Y, Ge C J 2009 Acta Phys. Sin. 58 1456 (in Chinese) [闵富红, 余杨, 葛曹君 2009 58 1456]
[36] [37] [38] Wu Z M, Xie J Y 2007 Chin. Phys. 16 1901
[39] Fu J, Yu M, Ma T D 2011 Chin. Phys. B 20 120508
[40] [41] Hu J B, Han Y, Zhao L D 2007 Acta Phys. Sin. 58 2235 (in Chinese) [胡建兵,韩焱,赵灵冬 2009 58 2235]
[42] [43] [44] Matignon D 1996 IMACS, IEEE SMC Proceedings Conference Lille, France, July 9-12, 1996 p963
[45] [46] Lu J G 2005 Chaos Soliton. Fract. 26 1125
[47] Gao T G, Chen Z Q, Yuan Z Z, Yu D C 2007 Chaos Soliton. Fract. 33 922
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[1] [2] Gao X, Yu J B 2005 Chin. Phys. 14 908
[3] [4] Lu J G 2006 Physica A 359 107
[5] Yu Y G, Li H X, Wang S 2009 Chaos Soliton. Fract. 42 1181
[6] [7] [8] Li C G, Chen G R 2004 Physica A 341 55
[9] [10] Lu J G 2006 Phys. Lett. A 354 305
[11] [12] Pecora L M, Carroll T L 1990 Phys. Rev. Lett. 64 821
[13] [14] Zhang H G, Ma T D, Huang G B, Wang Z L 2010 IEEE Trans. Syst. Man Cybern. B 40 831
[15] [16] Wang M J, Wang X Y 2011 Int. J. Mod. Phys. B 25 1283
[17] [18] Ma T D, Fu J, Sun Y 2010 Chin. Phys. B 19 090502
[19] [20] Wang X Y, Liu R, Zhang N 2011 Commun. Theor. Phys. 55 617
[21] 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 58 6039]
[22] [23] Chen L P, Chai Y, Wu R C 2011 Phys. Lett. A 375 2099
[24] [25] Wang M J, Wang X Y, Niu Y J 2011 Chin. Phys. B 20 010508
[26] [27] [28] Wang X Y, Zhang Y L, Lin D, Zhang N 2011 Chin. Phys. B 20 030506
[29] Niu Y J, Wang X Y, Nian F Z, Wang M J 2010 Chin. Phys. B 19 120507
[30] [31] [32] Jia L X, Dai H, Hui M 2010 Chin. Phys. B 19 110509
[33] Chen X R, Liu C X, Wang F Q, Li Y X 2008 Acta Phys. Sin. 57 1416 (in Chinese) [陈向荣,刘崇新,王发强,李永勋 2008 57 1416]
[34] [35] Min F H, Yu Y, Ge C J 2009 Acta Phys. Sin. 58 1456 (in Chinese) [闵富红, 余杨, 葛曹君 2009 58 1456]
[36] [37] [38] Wu Z M, Xie J Y 2007 Chin. Phys. 16 1901
[39] Fu J, Yu M, Ma T D 2011 Chin. Phys. B 20 120508
[40] [41] Hu J B, Han Y, Zhao L D 2007 Acta Phys. Sin. 58 2235 (in Chinese) [胡建兵,韩焱,赵灵冬 2009 58 2235]
[42] [43] [44] Matignon D 1996 IMACS, IEEE SMC Proceedings Conference Lille, France, July 9-12, 1996 p963
[45] [46] Lu J G 2005 Chaos Soliton. Fract. 26 1125
[47] Gao T G, Chen Z Q, Yuan Z Z, Yu D C 2007 Chaos Soliton. Fract. 33 922
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