具有完全不确定参数的五项双曲型混沌系统的投影同步

余飞; 王春华; 胡燕; 尹晋文

doi:10.7498/aps.61.060505

摘要

提出了一个新的简单的双曲型三维自治混沌系统,该三维混沌系统只含有五项, 并且其非线性特征主要依赖于一个非线性二次双曲正弦项和一个非线性二次交叉项. 较已有的三维混沌系统而言, 不仅系统的项要少一些, 而且在参数变化时, 呈现混沌的参数范围也很大. 对系统的一些基本动力学特性进行了数值模拟和理论分析. 同时, 还研究了具有完全不确定参数的该五项双曲型混沌系统的投影同步. 基于Lyapunov指数稳定性理论和Barbalat引理, 设计了一个新的具有参数自适应律的自适应同步控制器, 利用该控制器分别实现了两个结构相同和相异混沌系统的渐进性和全局性投影同步. 数值模拟验证了该方法的有效性和可行性.

关键词:

Abstract

A new simple hyperbolic-type three-dimensional autonomous chaotic system is proposed. It is of interest that the chaotic system has only five terms which mainly rely on a nonlinear quadratic hyperbolic sine term and a quadratic cross-product term. Compared with other three-dimensional chaotic systems, the new system has not only less terms, but also a wider range of chaos when the parameter varies. Basic dynamical properties of the system are studied by numerical and theoretical analysis. Moreover the projective synchronization of the five-term hyperbolic-type chaotic system with fully uncertain parameters is also investigated in this paper. Based on Lyapunov stability theory and Barbalat's lemma, a new adaptive controller with parameter update law is designed to projectivly synchronize two chaotic systems asymptotically and globally, including two identical exponential-type chaotic systems and two non-identical chaotic systems. Numerical simulations show the effectiveness and the feasibility of the developed methods.

Keywords:

three-dimensional autonomous chaotic system /
five-term hyperbolic-type chaotic system /
projective synchronization /
adaptive controller

作者及机构信息

1.
湖南大学信息科学与工程学院, 长沙 410082

通信作者: 王春华, wch1227164@sina.com

Authors and contacts

1.
College of Information Science and Engineering, Hunan University, Changsha 410082, China

Corresponding author: Wang Chun-Hua, wch1227164@sina.com

参考文献

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施引文献

[1]	Han J J, Fu W J 2010 Chin. Phys. B 19 010205
[2]	Di G H, Xu Y, Xu W, Gu R C 2011 Acta Phys. Sin. 60 020504 (in Chinese)[狄根虎, 许勇, 徐伟, 顾仁财 2011 60 020504]
[3]	Liu Y M, Zhang Y H, Yang J Q 2009 J. Circuits Syst. 14 116 (in Chinese)[刘玉民, 张雨虹, 杨金泉 2009 电路与系统学报 14 116]
[4]	Huang C H, Lin C H, Kuo C L 2011 IEEE Trans. Power Delivery 26 944
[5]	Lorenz E N 1963 J. Atmos. Sci. 20 130
[6]	R? ssler O E 1976 Phys. Lett. A 57 397
[7]	Chen G, Ueta T 1999 Int. J. Bifur. Chaos 9 1465
[8]	Lü J, Chen G 2002 Int. J. Bifur. Chaos 12 659
[9]	Lü J, Chen G, Cheng D, Celikovsky S 2002 Int. J. Bifur. Chaos 12 2917
[10]	Celikovsky S, Chen G 2002 Int. J. Bifur. Chaos 12 1789
[11]	Liu C, Liu T, Liu L, Liu K 2004 Chaos, Solitons and Fractals 22 1031
[12]	Pecora L M, Carroll T L 1990 Phys. Rev. Lett. 64 821
[13]	Pan L, Zhou W, Zhou L, Sun K 2011 Commun. Nonlinear Sci. Numer. Simulat. 16 2628
[14]	Liu Y Z, Jiang C S, Lin C S 2008 Acta Phys. Sin. 57 709 (in Chinese)[刘扬正, 姜长生, 林长圣 2008 57 709]
[15]	Wang F Q, Liu C X 2006 Acta Phys. Sin. 55 5055 (in Chinese)[王发强, 刘崇新 2006 55 5055]
[16]	Xu F, Yu P 2010 J. Math. Anal. Appl. 362 252
[17]	Chen Z S, Sun K H, Zhang T S 2005 Acta Phys. Sin. 54 2580 (in Chinese)[陈志盛, 孙克辉, 张泰山 2005 54 2580]
[18]	Liu Y Z, Jiang C S, Lin C S, Jiang Y M 2007 Chin. Phys. 16 660
[19]	Wu X J, Wang X Y 2006 Acta Phys. Sin. 55 6261 (in Chinese)[武相军, 王兴元 2006 55 6261]
[20]	Cai G L, Huang J J 2006 Acta Phys. Sin. 55 3997 (in Chinese)[蔡国梁,黄娟娟 2006 55 3997]
[21]	Wang F Q, Liu C X 2006 Chin. Phys. 15 1971
[22]	Guo H J, Yin Y W, Wang H M 2008 Chin. Phys. B 17 1652
[23]	Li X C, Xu W, Xiao Y Z 2008 Acta Phys. Sin. 57 4721 (in Chinese)[李秀春, 徐伟, 肖玉柱 2008 57 4721]
[24]	Hua C C, Guan X P 2004 Chin. Phys. 13 1391
[25]	Chen X R, Liu C X, Li Y X 2008 Acta Phys. Sin. 57 1453 (in Chinese)[陈向荣, 刘崇新, 李永勋 2008 57 1453]
[26]	Njah A N 2010 Nonlinear Dyn. 61 1
[27]	Lü L, Zhang Q L, Guo Z A 2008 Chin. Phys. B 17 0498
[28]	Zheng H Q, Jing Y W 2011 Chin. Phys. B 20 060504
[29]	Zhang Q, L¨u J, Chen S 2010 Commun. Nonlinear Sci. Numer. Simulat. 15 3067
[30]	Li X F, Leung A C S, Han X P, Liu X J, Chu Y D 2011 Nonlinear Dyn. 63 263
[31]	Taghvafard H, Erjaee G H 2011 Commun. Nonlinear Sci. Numer. Simulat. 16 4079
[32]	Hu M F, Xu Z Y 2007 Chin. Phys. 16 3231
[33]	Cai N, Jing Y, Zhang S 2010 Commun. Nonlinear Sci. Numer. Simulat. 15 1613
[34]	Ghosh D, Bhattacharya S 2010 Nonlinear Dyn. 61 11
[35]	Dai H, Jia L X, Hui M, Si G Q 2011 Chin. Phys. B 20 040507

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