非线性耦合对线性耦合同步的调制研究

李凡; 靳伍银; 马军

doi:10.7498/aps.61.240501

摘要

基于李亚普诺夫稳定性理论, 构造了指数型的李亚普诺夫函数, 以四变量的Chen超混沌系统为例, 解析地证明了线性耦合实现同步的可靠性. 进一步研究了非线性耦合对线性耦合同步的调制作用. 基于无量纲化的动力学方程定义一个统计函数来估算控制器的消耗功率, 确定了线性耦合与非线性耦合实现同步对应的参数范围, 数值计算结果验证了理论结果的可靠性.

关键词:

Based on the Lyapunov stability theory, the Lyapunov function in the form of exponential type is constructed. The four-variable Chen hyperchaotic model is investigated as an example. The reliability of a linear coupling-inudced synchronization of hyperchaotic system is proofed analytically. Furthermore, the modulation effect of nonlinear coupling on the synchronization induced by linear coupling is investigated. A statictical function is defined to evaulate the power consumption of controller according to the dimensionaless dynamical equations, the appropriate parameter region for synchronization due to the joint action of linear and nonlinear coupling, and the extensive numerical results confirm the correctress of the theoretical predication.

Keywords:

作者及机构信息

1.
兰州理工大学物理系, 兰州 730050;

2.
兰州理工大学机电学院, 兰州 730050

基金项目: 国家自然科学基金(批准号: 11072099, 11265008)资助的课题.

Authors and contacts

1.
Department of Physics, Lanzhou University of Technology, Lanzhou 730050, China;

2.
College of Mechano-Electronic Engineering, Lanzhou University of Technology, Lanzhou 730050, China

Funds: Project supported by the National Natural and Science Foundation of China (Grant Nos. 11072099, 11265008).

参考文献

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[13]	Li X W, Zheng Z G 2007 Commun. Theor. Phys. 47 265
[14]	Yang X L, Xu W 2008 Chin. Phys. B 17 2004
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[16]	Wang X H, Jiao L C, Wu J S 2010 Chin. Phys. B 19 020501
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[25]	Zhou P, Kuang F 2010 Acta Phys. Sin. 59 6851 (in Chinese) [周平, 邝菲 2010 59 6851]
[26]	Jia F L, Xu W 2007 Acta Phys. Sin. 56 3106 (in Chinese) [贾飞蕾, 徐伟 2007 56 3101]
[27]	Taherion S, Lai Y C 2000 Int. J. Bifurcat Chaos 11 2587
[28]	Sun Z K, Yang X L 2011 Chaos 21 033114
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[30]	Li C D, Liao X F 2004 Phys. Lett. A 329 301
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[43]	Moujahid A, d'Anjou A, Torrealdea F J 2011 Chaos, Solitons & Fractals 44 92
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[45]	Sarasola C, Torrealdea F J , d'Anjou A 2002 Math. Comput. Simulat. 58 309
[46]	Sarasola C 2005 Phys. Rev. E 72 026223

施引文献

[1]	Zhan M, Wang X G, Gong X F 2003 Phys. Rev. E 68036208
[2]	Yuan Z L, Xu Z Y, Guo L X 2011 Chin. Phys. B 20 070503
[3]	Li F, Liu Q R, Guo H Y 2012 Nolinear Dynam 69 2169
[4]	Liu Z H, Zhou J, Munakata T 2009 EPL 87 50002
[5]	Jia L X, Dai H, Hui M 2010 Chin. Phys. B 19 100501
[6]	Li D, Zheng Z G 2008 Chin. Phys. B 17 4009
[7]	Wang Z S, Zhang H G, Wang Z L 2006 Acta. Phys. Sin. 55 (in Chinese) 2687 [王占山, 张化光, 王智良 2006 55 2687]
[8]	Ma J, Li F, Huang L 2011 Commun. Nonlinear Sci. Numer Simulat 16 3770
[9]	Chen Y, Wu X F, Gui Z F 2010 Appl. Math. Model. 34 4161
[10]	Rosenblum M G, Pikovsky A S, Kurths J 1996 Phys. Rev. Lett. 76 1804
[11]	Zhan M, Hu G, Wang X G 2000 Chin. Phys. Lett. 17 332
[12]	Zheng Z G, Hu G, Zhou C S 2000 Acta. Phys. Sin. 49 2320 (in Chinese) [郑志刚, 胡岗, 周昌松等 2000 49 2320]
[13]	Li X W, Zheng Z G 2007 Commun. Theor. Phys. 47 265
[14]	Yang X L, Xu W 2008 Chin. Phys. B 17 2004
[15]	Wei D Q, Luo X S, Qin Y H 2009 Chin. Phys. B 18 2184
[16]	Wang X H, Jiao L C, Wu J S 2010 Chin. Phys. B 19 020501
[17]	Wang H X, Lu Q S, Shi X 2010 Chin. Phys. B 19 060509
[18]	Fell J, Axmacher N 2011 Nature Rev. Neurosci 12 105
[19]	Taghvafard H., Erjaee G H 2011 Commun. Nonlinear Sci. Numer Simulat 16 4078
[20]	Wang Z L, Shi X R 2012 Nonlinear Dynam. 67 1817
[21]	Wang Z L, Shi X R 2011 Commun. Nonlinear Sci. Numer Simulat 16 463
[22]	Li D, Deng L M, Du Y X 2012 Acta Phys. Sin. 61 050502 (in Chinese) [李东, 邓良民, 杜永霞, 杨媛媛 2012 61 050502]
[23]	Zhang R X, Tian G, Li P 2008 Acta Phys. Sin. 57 2080 (in Chinese) [张若洵, 田钢, 栗苹, 杨世平 2008 57 2073]
[24]	Luo Q, Gao Y, Qi Y N 2009 Acta Phys. Sin. 58 6809 (in Chinese) [罗群, 高雅, 齐雅楠, 高雅2, 吴桐, 许欢, 李丽香, 杨义先 2009 58 6809]
[25]	Zhou P, Kuang F 2010 Acta Phys. Sin. 59 6851 (in Chinese) [周平, 邝菲 2010 59 6851]
[26]	Jia F L, Xu W 2007 Acta Phys. Sin. 56 3106 (in Chinese) [贾飞蕾, 徐伟 2007 56 3101]
[27]	Taherion S, Lai Y C 2000 Int. J. Bifurcat Chaos 11 2587
[28]	Sun Z K, Yang X L 2011 Chaos 21 033114
[29]	Tong S C, Zhang H G, Ma T D 2009 Chin. Phys. B 18 3751
[30]	Li C D, Liao X F 2004 Phys. Lett. A 329 301
[31]	Wang Q Y, Lu Q S, Duan Z S 2010 Int. J. Nonlinear Mecha. 45 640
[32]	Kinzel W, Englert A, Kanter I 2010 Phil. Trans. R. Soc. A 368 379
[33]	Kocarev L, Parlitz U 1995 Phys. Rev. Lett. 74 5028
[34]	Peng J H, Ding E J, Ding M 1996 Phys. Rev. Lett. 76 904
[35]	VanWigiggeren G D, Roy R 1998 Science 279 1198
[36]	Perc M, Marhl M 2003 Chem. Phys. Lett. 376 432
[37]	Ning C Z, Haken H 1990 Phys. Rev. A 41 3826
[38]	Kapitaniak T, Chua L O 1994 Int. J. Bifurcat Chaos 4 477
[39]	Chen G, Dong X 1998 World Scientific Pub. Co. 2 132
[40]	Pinto R D, Varona P, Volkovskii A R 2000 Phys. Rev. E 62 2644
[41]	Torrealdea F J, d'Anjou A, Graña M 2006 Phys. Rev. E 74 011905
[42]	Rech P C 2011 Phys. Lett. A 375 1461
[43]	Moujahid A, d'Anjou A, Torrealdea F J 2011 Chaos, Solitons & Fractals 44 92
[44]	Moujahid A, d'Anjou A, Torrealdea F J 2011 Phys. Rev. E 83 031912
[45]	Sarasola C, Torrealdea F J , d'Anjou A 2002 Math. Comput. Simulat. 58 309
[46]	Sarasola C 2005 Phys. Rev. E 72 026223

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