Reliability of linear coupling synchronization of hyperchaotic systems with unknown parameters

doi:10.1088/1674-1056/22/10/100502

中国物理B ›› 2013, Vol. 22 ›› Issue (10): 100502-100502.doi: 10.1088/1674-1056/22/10/100502

Reliability of linear coupling synchronization of hyperchaotic systems with unknown parameters

李凡, 王春妮, 马军

Department of Physics, Lanzhou University of Technology, Lanzhou 730050, China

收稿日期:2013-02-19 修回日期:2013-04-01 出版日期:2013-08-30 发布日期:2013-08-30
基金资助:
Project supported partially by the National Natural Science Foundation of China (Grant No. 11265008).

Reliability of linear coupling synchronization of hyperchaotic systems with unknown parameters

Li Fan (李凡), Wang Chun-Ni (王春妮), Ma Jun (马军)

Department of Physics, Lanzhou University of Technology, Lanzhou 730050, China

Received:2013-02-19 Revised:2013-04-01 Online:2013-08-30 Published:2013-08-30
Contact: Ma Jun E-mail:hyperchaos@163.com
Supported by:
Project supported partially by the National Natural Science Foundation of China (Grant No. 11265008).

摘要/Abstract

摘要： Complete synchronization could be reached between some chaotic and/or hyperchaotic systems under linear coupling. More generally, the conditional Lyapunov exponents are often calculated to confirm the stability of synchronization and reliability of linear controllers. In this paper, detailed proof and measurement of the reliability of linear controllers are given by constructing a Lyapunov function in the exponential form. It is confirmed that two hyperchaotic systems can reach complete synchronization when two linear controllers are imposed on the driven system unidirectionally and the unknown parameters in the driving systems are estimated completely. Finally, it gives the general guidance to reach complete synchronization under linear coupling for other chaotic and hyperchaotic systems with unknown parameters.

关键词: parameter estimation, exponential Lyapunov function, parameter observer, linear coupling

Abstract: Complete synchronization could be reached between some chaotic and/or hyperchaotic systems under linear coupling. More generally, the conditional Lyapunov exponents are often calculated to confirm the stability of synchronization and reliability of linear controllers. In this paper, detailed proof and measurement of the reliability of linear controllers are given by constructing a Lyapunov function in the exponential form. It is confirmed that two hyperchaotic systems can reach complete synchronization when two linear controllers are imposed on the driven system unidirectionally and the unknown parameters in the driving systems are estimated completely. Finally, it gives the general guidance to reach complete synchronization under linear coupling for other chaotic and hyperchaotic systems with unknown parameters.

Key words: parameter estimation, exponential Lyapunov function, parameter observer, linear coupling

中图分类号: (Nonlinear dynamics and chaos)

05.45.-a

李凡, 王春妮, 马军. Reliability of linear coupling synchronization of hyperchaotic systems with unknown parameters[J]. 中国物理B, 2013, 22(10): 100502-100502.

Li Fan (李凡), Wang Chun-Ni (王春妮), Ma Jun (马军). Reliability of linear coupling synchronization of hyperchaotic systems with unknown parameters[J]. Chin. Phys. B, 2013, 22(10): 100502-100502.

参考文献 60

[1]	Boccaletti S, Grebogi C, Lai Y C, Lai Y C, Mancini H and Maza D 2000 Phys. Rep. 329 103
[2]	Boccaletti S, Kurths J, Osipov G, Valladares D L and Zhou C S 2002 Phys. Rep. 366 1
[3]	Rössler O E 1979 Phys. Lett. A 71 155
[4]	Liu C X and Liu L 2009 Chin. Phys. B 18 2188
[5]	Perc M and Marhl M 2003 Biophys. Chem. 104 509
[6]	Krese B, Perc M and Govekar E 2010 Chaos 20 013129
[7]	Yang N N, Liu C X and Wu C J 2010 Chin. Phys. B 19 100502
[8]	Krese B, Perc M and Govekar E 2011 Int. J. Bifurc. Chaos 21 1689
[9]	Lü J H and Chen G R 2006 Int. J. Bifurc. Chaos 16 775
[10]	Yu S M, Lü J H, Chen G R and Xu X H 2012 IEEE Trans. Circ. Syst. I 59 1015
[11]	Kanso A, Yahyaoui H and Almulla M 2012 Informat. Sci. 186 249
[12]	Li D, Hu G and Wang S H 2012 Commun. Nonlinear Sci. Numer. Simul. 17 2579
[13]	Huang Z Q 2011 Commun. Nonlinear Sci. Numer. Simul. 16 3245
[14]	Ahmed F, Siyal M Y and Abbas V U 2010 Commun. Nonlinear Sci. Numer. Simul. 15 1338
[16]	Raphael C W and Wagner D 2006 Computers & Security 25 131
[17]	Stinson D R, Wei R and Chen K 2008 J. Combinatorial Theory Series A 115 105
[18]	Hirai Y, Kurokawa T, Matsuo S, Tanaka H and Yamamura A 2008 IEICE Trans. Fundamentals Electron. 91 64
[19]	Kocarev L and Parlitz U 1995 Phys. Rev. Lett. 74 5028
[20]	Boccaletti S, Farini A and Arecchi F T 1997 Phys. Rev. E 55 4979
[21]	d’Anjou A, Sarasola C, Torrealdea F J, Orduna R and Graña M 2001 Phys. Rev. E 63 046213
[22]	Mata-Machuca J L, Martínez-Guerra R and Aguilar-López R 2012 Commun. Nonlinear Sci. Numer Simul. 17 1706
[23]	Wu D and Li J J 2010 Chin. Phys. B 19 120505
[24]	Wang X Y, Zhang N, Ren X L and Zhang Y L 2011 Chin. Phys. B 20 020507
[25]	Moskalenko O I, Koronovskii A A and Hramov A E 2010 Phys. Lett. A 374 2925
[26]	Zhu H B, Qiu F and Cui B T 2010 Chin. Phys. B 19 030515
[27]	Volman V, Perc M and Bazhenov M 2011 PLoS One 6 e20572
[28]	Wang Q Y, Chen G R and Perc M 2011 PLOS One 6 e15851
[29]	Wang Q Y, Perc M, Duan Z S and Chen G R 2010 Physica A 389 3299
[30]	Fell J and Axmacher N 2011 Nat. Rev. Neurosci. 12 105
[31]	Torrealdea F J, Sarasola C, d’Anjou A, Moujahid A and Vélez de Mendizábal N 2009 BioSysts. 97 60
[32]	Rosenblum M G, Pikovsky A S and Kurths J 1996 Phys. Rev. Lett. 76 1804
[33]	Rosenblum M G, Pikovsky A S and Kurths J 1997 Phys. Rev. Lett. 78 4193
[34]	Wang Z L 2009 Commun. Nonlinear Sci. Numer. Simul. 14 2366
[35]	Li F, Liu Q R, Guo H Y, Zhao Y H, Tang J and Ma J 2012 Nonlinear Dyn. 69 2169
[36]	Ma J, Zhang A H, Xia Y F and Zhang L P 2010 Appl. Math. Comput. 215 3318
[37]	Wang C N, Ma J and Jin W Y 2012 Dyn. Syst. 27 253
[38]	Mainieri R and Rehacek J 1999 Phys. Rev. Lett. 82 3042
[39]	Boulkroune A and M’saad M 2012 J. Vib. Control 18 437
[40]	Luo R Z, Deng S C and Wei Z M 2010 J. Vib. Control 17 1099
[41]	Wei W, Li D H and Wang J 2010 Chin. Phys. B 19 040507
[42]	Liu W B, Wallace K S and Chen G R 2011 Chin. Phys. B 20 090510
[43]	Lü J H and Chen G R 2002 Int. J. Bifurc. Chaos 12 659
[44]	Li X W and Zheng Z G 2007 Commun. Theor. Phys. 47 265
[45]	Tamasevicius A and Cenys A 1997 Phys. Rev. E 55 297
[46]	Lü J H and Chen G R 2005 IEEE Trans. Autom. Control 50 841
[47]	Squartini S, Lü J H and Wei Q L 2013 Neural Comput. Appl. 22 203
[48]	Lu X Q, Lu R Q, Chen S H and Lü J H 2013 IEEE Trans. Circ. Syst. I 60 352
[49]	Li Z and Han C Z 2001 Chin. Phys. 10 494
[50]	Li Z and Han C Z 2002 Chin. Phys. 11 9
[51]	Chen S H, Zhao L M and Liu J 2002 Chin. Phys. 11 543
[52]	Mu J, Tao C and Du G H 2003 Chin. Phys. 12 381
[53]	Sang J Y, Yang J and Yue L J 2011 Chin. Phys. B 20 080507
[54]	Zhang R X and Yang S P 2011 Chin. Phys. B 20 090512
[55]	Huang D X and Wang J Y 2008 Acta Phys. Sin. 57 2755 (in Chinese)
[56]	Zeng Y C, Fu Z J and Chen Z 2008 Acta Phys. Sin. 57 46 (in Chinese)
[57]	Li L X, Yang Y X, Peng H P and Wang X D 2007 Acta Phys. Sin. 56 51 (in Chinese)
[58]	Li X T and Yin M H 2012 Chin. Phys. B 21 050507
[59]	Li N Q, Pan W, Yan L S and Luo B 2011 Chin. Phys. B 20 060502
[60]	Huang L L and Qi X 2013 Acta Phys. Sin. 62 080507 (in Chinese)

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Reliability of linear coupling synchronization of hyperchaotic systems with unknown parameters

Reliability of linear coupling synchronization of hyperchaotic systems with unknown parameters

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