分数阶系统有限时间稳定性理论及分数阶超混沌Lorenz系统有限时间同步

赵灵冬; 胡建兵; 包志华; 章国安; 徐晨; 张士兵

doi:10.7498/aps.60.100507

摘要

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.

关键词:

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:

作者及机构信息

1.
南通大学电子信息学院,南通 226019

基金项目: 国家自然科学基金(批准号: 50875132)和南通大学自然科学基金(批准号: 10Z021)资助的课题.

Authors and contacts

1.
School of Electronics & Information, Nantong University, Nantong 226019, China

参考文献

[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)

施引文献

[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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