A finite-time stable theorem about fractional systems and finite-time synchronizing fractional super chaotic Lorenz systems

Zhao Ling-Dong; Hu Jian-Bing; Bao Zhi-Hua; Zhang Guo-An; Xu Chen; Zhang Shi-Bing

doi:10.7498/aps.60.100507

Abstract

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:

Authors and contacts

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

References

[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
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[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]
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[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 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)

Cited By

[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 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 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 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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Vol. 60, Issue 10 - 2011-05-20

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A finite-time stable theorem about fractional systems and finite-time synchronizing fractional super chaotic Lorenz systems

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A finite-time stable theorem about fractional systems and finite-time synchronizing fractional super chaotic Lorenz systems

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