Studying the intermittent stable theorem and the synchronization of a delayed fractional nonlinear system

doi:10.1088/1674-1056/22/8/080506

Abstract In this paper, an intermittent synchronizing delayed fractional nonlinear system is studied. We propose a novel intermittent stable theorem for the delayed fractional system and derive a new synchronization criterion for delayed fractional systems by means of fractional stable theorem and the differential inequality method. Intermittent synchronizing fractional delayed Newton-Leipnik system is taken as an illustrative example and numerical simulation of this example is presented to show the feasibility and effectiveness of the proposed theorem.

Keywords: fractional delay stability intermittent synchronization

Received: 25 December 2012
Revised: 13 May 2013
Accepted manuscript online:

PACS:	05.45.Gg	(Control of chaos, applications of chaos)
	05.45.Xt	(Synchronization; coupled oscillators)

Fund: Project supported by Jiangsu Overseas Research & Training Program for University Prominent Young & Middle-aged Teachers and Presidents and the National Natural Science Foundation of China (Grant No. 61171077).

Corresponding Authors: Zhao Ling-Dong
E-mail: zhaolingdong@163.com

Cite this article:

Hu Jian-Bing (胡建兵), Zhao Ling-Dong (赵灵冬), Xie Zheng-Guang (谢正光) Studying the intermittent stable theorem and the synchronization of a delayed fractional nonlinear system 2013 Chin. Phys. B 22 080506

[1]	Dejardin J L 2003 Phys. Rev. E 68 031108
[2]	Tarasov V E 2009 Theor. Math. Phys. 158 355
[3]	Jumarie G 2010 Kybernetes 39 1167
[4]	Choudhury M D, Chandra S and Nag S 2012 Colloid Surface A 407 64
[5]	Dial O E, Ashoori R C, Pfeiffer L N and West K W 2010 Nature 464 566
[6]	Casasanta G and Garra R 2012 Signal Image Video P 6 389
[7]	Aghababa M P 2012 Chin. Phys. B 21 100505
[8]	He J H 2012 Abstr. Appl. Anal. DOI: 10.1155/2012/916793
[9]	Aydiner E 2005 Phys. Rev. E 71 6103
[10]	He J H 2012 Therm. Sci. 2 331
[11]	He J H2012 Math. Probl. Eng. DOI: 10.1155/2012/394212
[12]	Li Y, Chen Y Q and Podlubny I 2010 Comput. Math. Appl. 59 1810
[13]	Wong W K, Li H J and Leung S Y S 2012 Commun. Nonlinear Sci. Numer. Simul. 17 4877
[14]	Wang F Q and Ma X K 2013 Chin. Phys. B 22 030506
[15]	Gepreel K A and Omran S 2012 Chin. Phys. B 21 110204
[16]	Si G Q, Sun Z Y, Zhang Y B 2012 Nonlinear Anal. Real World Appl. 13 1761
[17]	Chen D Y, Zhang R F and Sprott J C 2012 Chaos 22
[18]	Hegazi A S, Ahmed E and Matouk A E 2013 Commun. Nonlinear Sci. Numer. Simul. 18 1193
[19]	Luo C and Wang X Y 2013 Nonlinear Dyn. 71 241
[20]	Park M J, Kwon O M and Park J H 2011 Appl. Math. Comput. 217 7197
[21]	Esfanjani R M and Nikravesh S K Y 2009 Iet Control Theory A 3 1395
[22]	Senthilkumar D V, Kurths J and Lakshmanan M 2009 Phys. Rev. E 79 066208
[23]	Lu J G 2006 Chin. Phys. 15 301
[24]	Lin T C and Lee T Y 2011 IEEE T. Fuzzy Syst. 19 623
[25]	Pecora L and Carroll T 1990 Phys. Rev. Lett. 64 821
[26]	Fu S H, Lu Q S and Du Y 2012 Chin. Phys. B 21 060507
[27]	Ye Z Y, Yang G and Deng C B 2011 Chin. Phys. B 20 010207
[28]	Guo X Y and Li J M 2012 Commun. Nonlinear Sci. Numer. Simul. 17 4395
[29]	Fu J, Yu M and Ma T D 2011 Chin. Phys. B 20 120508
[30]	Zhang Q J, Luo J and Wan L 2013 Nonlinear Dyn. 71 353
[31]	Wang Y J, Hao J N and Zuo Z Q 2010 Commun. Theor. Phys. 54 679
[32]	Huang J J, Li C D, Zhang W and Wei P C 2012 Chin. Phys. B 21 090508
[33]	Podlubny I 1999 Fractional Differential Equations (New York: Academic Press)
[34]	Caputo M 1967 II, Geophys. J. R. Astron. Soc. 13 529
[35]	Zhao L D, Hu J B and Fang J A 2012 Nonlinear Dyn. 70 475
[36]	Wang X D and Tian L X 2006 Chaos, Solitons and Fractals 27 31

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