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Stability about fractional chaotic system is studied and a theory about fractional chaotic system is proposed and proved under intermittent control in this paper. Based on the theorem, a controller is designed to realize the intermittent synchronizing fractional unified chaotic system. Numerical simulation demonstrates the effectiveness of the theorem.
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Keywords:
- fractional /
- unified chaotic system /
- intermittent synchronization /
- stability
[1] Mandelbort B B 1983 The fractal Geometry of Nature (New York: Freeman)
[2] Yan X M,Liu D 2010 Acta Phys. Sin. 59 3403 (in Chinese) [阎晓妹、 刘 丁 2010 物理学报 59 3403]
[3] Huang L, Feng R,Wang M 2004 Phys. Lett. A 32 271
[4] Liu Y, Xie Y 2010 Acta Phys. Sin. 59 2147 (in Chinese) [刘 勇、 谢 勇 2010 物理学报 59 2147]
[5] 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 物理学报 57 1416]
[6] Zhao P D, Zhang X D 2008 Acta Phys. Sin 57 2791(in Chinese) [赵品栋、 张晓丹 2008 物理学报 57 2791]
[7] Tavazoei M S, Haeri M 2008 Physica A 387 57
[8] Hu J B, Han Y, Zhao L D 2009 Acta Phys. Sin. 58 1441 (in Chinese) [胡建兵、 韩 焱、 赵灵冬 2009 物理学报 58 1441]
[9] Li A, Chen G R 2004 Chaos Soliton. Fract. 22 549
[10] 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 物理学报 58 6039]
[11] Wang J W, Zhang Y B 2009 Phys. Lett. A 374 202
[12] Deng W H 2007 Phys. Rev. E 75 056201
[13] Vedat Suat Erturk,Shaher Momani,Zaid Odibat 2008 Commun. Nonlinear Sci. Num. Simulat. 13 1642
[14] Ricardo Almeida, Delfim F M Torres 2011 Commun. Nonlinear Sci. Num. Simulat. 16 1490
[15] Matignon D 1996 IEEE International Conferenceon Systems, Man and Cybernetics Lille, France July 9—12, 1996
[16] Yan J P, Li C P 2004 Chaos, Soliton. Fract. 22 443
[17] Deng W H 2007 J. Comput. Phys. 227 1510
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[1] Mandelbort B B 1983 The fractal Geometry of Nature (New York: Freeman)
[2] Yan X M,Liu D 2010 Acta Phys. Sin. 59 3403 (in Chinese) [阎晓妹、 刘 丁 2010 物理学报 59 3403]
[3] Huang L, Feng R,Wang M 2004 Phys. Lett. A 32 271
[4] Liu Y, Xie Y 2010 Acta Phys. Sin. 59 2147 (in Chinese) [刘 勇、 谢 勇 2010 物理学报 59 2147]
[5] 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 物理学报 57 1416]
[6] Zhao P D, Zhang X D 2008 Acta Phys. Sin 57 2791(in Chinese) [赵品栋、 张晓丹 2008 物理学报 57 2791]
[7] Tavazoei M S, Haeri M 2008 Physica A 387 57
[8] Hu J B, Han Y, Zhao L D 2009 Acta Phys. Sin. 58 1441 (in Chinese) [胡建兵、 韩 焱、 赵灵冬 2009 物理学报 58 1441]
[9] Li A, Chen G R 2004 Chaos Soliton. Fract. 22 549
[10] 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 物理学报 58 6039]
[11] Wang J W, Zhang Y B 2009 Phys. Lett. A 374 202
[12] Deng W H 2007 Phys. Rev. E 75 056201
[13] Vedat Suat Erturk,Shaher Momani,Zaid Odibat 2008 Commun. Nonlinear Sci. Num. Simulat. 13 1642
[14] Ricardo Almeida, Delfim F M Torres 2011 Commun. Nonlinear Sci. Num. Simulat. 16 1490
[15] Matignon D 1996 IEEE International Conferenceon Systems, Man and Cybernetics Lille, France July 9—12, 1996
[16] Yan J P, Li C P 2004 Chaos, Soliton. Fract. 22 443
[17] Deng W H 2007 J. Comput. Phys. 227 1510
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