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研究了分数阶系统有限时间稳定性理论及分数阶混沌系统的同步问题.根据分数阶微分性质及分数阶系统稳定性理论,建立了分数阶系统有限时间稳定性理论并进行了证明.根据该理论设计控制器实现了分数阶超混沌Lorenz系统有限时间同步并运用数值仿真进行了验证.
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关键词:
- 分数阶 /
- 超混沌Lorenz系统 /
- 稳定 /
- 有限时间同步
Finite-time stable theorem about fractional system and finite-time synchronizing fractional chaotic system are studied in this paper. A finite-time stable theorem is proposed and proved according to the properties of fractional equation. Using this theorem, fractional super chaotic Lorenz systems is synchronized in finite-time. Numerical simulation certifies the effectiveness of the theorem proposed in this paper.-
Keywords:
- fractional /
- super chaotic Lorenz system /
- stable /
- finite-time synchronizing
[1] Chen J R, Tao R J 2001 Journal of Shanghai University 5 292
[2] Chen W,Zhang X D, Korosak D. 2010 Int. J. Nonlin. Sci. Num. 11 3
[3] Li Z B 2010 Int. J. Nonlin. Sci. Num. 11 335
[4] Li Z B, He J H 2010 Mathematical & Computational Applications 15 970
[5] Cui B T, Ji Y, Qiu F 2009 Chin. Phys. B 18 5203
[6] Wu X J, Lu H T, Shen S L 2009 Phys. Lett. A 373 2329
[7] Mohammad Saleh Tavazoei, Mohammad Haeri 2008 Physica A 387 57
[8] Liu C X 2004 Chaos Solitons and Fractals 22 1031
[9] Jia H Y, Chen Z Q, Yuan Z Z 2010 Chin. Phys.B 19 507
[10] 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 物理学报 57 7522]
[11] Zhang R X, Yang S P 2009 Journal of Hebei Normal University 33 37 (in Chinese) [张若洵、杨世平 2009 河北师范大学学报 33 37]
[12] Vedat Suat Erturk,Shaher Momani,Zaid Odibat 2008 J. Cnsns 1642
[13] Liu Y F, Yang X G, Miu D, Yuan R P 2007 Acta Phys. Sin. 56 6250 (in Chinese) [刘云峰、杨小冈、缪 栋、袁润平 2007 物理学报 56 6250]
[14] Aghababa MP, Khanmohammadi S, Alizadeh G 2011 Applied Mathematical Modeling 35 3080
[15] Liu D, Yan X M 2009 Acta Phys. Sin. 58 3747 (in Chinese)[刘丁、闫晓妹 2009 物理学报 58 3747]
[16] Podlubny I 1999 Fractional differential equations (San Diego : Academic Press) p18
[17] He J H 2011 Thermal Science 15 145
[18] Matignon D. 1996 IMACS, IEEE-SMC, Lille (France)
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[1] Chen J R, Tao R J 2001 Journal of Shanghai University 5 292
[2] Chen W,Zhang X D, Korosak D. 2010 Int. J. Nonlin. Sci. Num. 11 3
[3] Li Z B 2010 Int. J. Nonlin. Sci. Num. 11 335
[4] Li Z B, He J H 2010 Mathematical & Computational Applications 15 970
[5] Cui B T, Ji Y, Qiu F 2009 Chin. Phys. B 18 5203
[6] Wu X J, Lu H T, Shen S L 2009 Phys. Lett. A 373 2329
[7] Mohammad Saleh Tavazoei, Mohammad Haeri 2008 Physica A 387 57
[8] Liu C X 2004 Chaos Solitons and Fractals 22 1031
[9] Jia H Y, Chen Z Q, Yuan Z Z 2010 Chin. Phys.B 19 507
[10] 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 物理学报 57 7522]
[11] Zhang R X, Yang S P 2009 Journal of Hebei Normal University 33 37 (in Chinese) [张若洵、杨世平 2009 河北师范大学学报 33 37]
[12] Vedat Suat Erturk,Shaher Momani,Zaid Odibat 2008 J. Cnsns 1642
[13] Liu Y F, Yang X G, Miu D, Yuan R P 2007 Acta Phys. Sin. 56 6250 (in Chinese) [刘云峰、杨小冈、缪 栋、袁润平 2007 物理学报 56 6250]
[14] Aghababa MP, Khanmohammadi S, Alizadeh G 2011 Applied Mathematical Modeling 35 3080
[15] Liu D, Yan X M 2009 Acta Phys. Sin. 58 3747 (in Chinese)[刘丁、闫晓妹 2009 物理学报 58 3747]
[16] Podlubny I 1999 Fractional differential equations (San Diego : Academic Press) p18
[17] He J H 2011 Thermal Science 15 145
[18] Matignon D. 1996 IMACS, IEEE-SMC, Lille (France)
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