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In this paper, the synchronization of fractional-order chaotic systems is investigated. Based on sliding mode control and adaptive control theory, a fractional order integral sliding surface with strong robustness is designed, and an adaptive sliding controller is proposed for synchronizing the fractional-order chaotic systems with retaining the nonlinear part. Numerical simulations on synchronizing the Chen chaotic systems, the Liu chaotic systems, and Arneodo chaotic systems are carried out separately. The simulation results show the validity and feasibility of the adaptive sliding controller.
[1] Ott E, Grebogi C, Yorke J A 1990 Phys. Rev. Lett. 64 1196
[2] Ditto W L, Rauseo S N, Spano M L 1990 Phys. Rev. Lett. 65 3211
[3] Chen S, L J 2002 Chaos Solition. Fract. 14 643
[4] Wang C, Su J 2004 Chaos Solition. Fract. 20 967
[5] Gao X, Yu J B 2005 Chaos Solition. Fract. 26 141
[6] Zhang H G, Fu J, Ma T D, Tong S C 2009 Chin. Phys. B 18 969
[7] Liang C X, Tang J S 2008 Chin. Phys. B 17 135
[8] Huang L L, Ma N 2012 Acta Phys. Sin. 61 160510 (in Chinese) [黄丽莲, 马楠 2012 物理学报 61 160510]
[9] Niu H, Zhang G S 2013 Acta Phys. Sin. 62 130502 (in Chinese) [牛弘, 张国山 2013 物理学报 62 130502]
[10] Yu Y G, Wen G G, Li H X, Diao M 2009 Int. J. Nonlinear Sci. Num. 10 379
[11] Faieghi M R, Delavari H 2012 Commum. Nolinear Sci. Numer. Simulat. 17 731
[12] Wang X Y, He Y J 2008 Phys. Lett. A 372 435
[13] Li C P, Deng W H 2006 Int. J. Modern Phys. B 20 791
[14] Deng W H 2007 Phys. Rev.E 75 056201
[15] Li Z, Han C Z 2002 Chin. Phys. 11 666
[16] Mohammad S T, Mohammad H 2008 Physica A 387 57
[17] Cao H F, Zhang R X 2011 Acta Phys. Sin. 60 050510 (in Chinese) [曹鹤飞, 张若徇 2011 物理学报 60 050510]
[18] Wu X J, Li J, Chen G R 2008 J. Franklin Institute 345 392
[19] Ahamd W M, Sprott J C 2003 Chaos Soliton. Fract. 16 339
[20] Sun K H, Ren J, Shang F 2008 Comput. Simulat. 25 312 (in Chinese) [孙克辉, 任健, 尚芳 2008 计算机仿真 25 312]
[21] Liu C X, Liu L, Liu K 2004 Chaos Soliton. Fract. 22 1031
[22] Lu J G 2005 Chaos Soliton. Fract. 26 1125
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[1] Ott E, Grebogi C, Yorke J A 1990 Phys. Rev. Lett. 64 1196
[2] Ditto W L, Rauseo S N, Spano M L 1990 Phys. Rev. Lett. 65 3211
[3] Chen S, L J 2002 Chaos Solition. Fract. 14 643
[4] Wang C, Su J 2004 Chaos Solition. Fract. 20 967
[5] Gao X, Yu J B 2005 Chaos Solition. Fract. 26 141
[6] Zhang H G, Fu J, Ma T D, Tong S C 2009 Chin. Phys. B 18 969
[7] Liang C X, Tang J S 2008 Chin. Phys. B 17 135
[8] Huang L L, Ma N 2012 Acta Phys. Sin. 61 160510 (in Chinese) [黄丽莲, 马楠 2012 物理学报 61 160510]
[9] Niu H, Zhang G S 2013 Acta Phys. Sin. 62 130502 (in Chinese) [牛弘, 张国山 2013 物理学报 62 130502]
[10] Yu Y G, Wen G G, Li H X, Diao M 2009 Int. J. Nonlinear Sci. Num. 10 379
[11] Faieghi M R, Delavari H 2012 Commum. Nolinear Sci. Numer. Simulat. 17 731
[12] Wang X Y, He Y J 2008 Phys. Lett. A 372 435
[13] Li C P, Deng W H 2006 Int. J. Modern Phys. B 20 791
[14] Deng W H 2007 Phys. Rev.E 75 056201
[15] Li Z, Han C Z 2002 Chin. Phys. 11 666
[16] Mohammad S T, Mohammad H 2008 Physica A 387 57
[17] Cao H F, Zhang R X 2011 Acta Phys. Sin. 60 050510 (in Chinese) [曹鹤飞, 张若徇 2011 物理学报 60 050510]
[18] Wu X J, Li J, Chen G R 2008 J. Franklin Institute 345 392
[19] Ahamd W M, Sprott J C 2003 Chaos Soliton. Fract. 16 339
[20] Sun K H, Ren J, Shang F 2008 Comput. Simulat. 25 312 (in Chinese) [孙克辉, 任健, 尚芳 2008 计算机仿真 25 312]
[21] Liu C X, Liu L, Liu K 2004 Chaos Soliton. Fract. 22 1031
[22] Lu J G 2005 Chaos Soliton. Fract. 26 1125
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