一类混沌系统同步时间可控的自适应投影同步

王春华; 胡燕; 余飞; 徐浩

doi:10.7498/aps.62.110509

摘要

基于自适应的方法, 提出了一种同步时间可控的混沌投影同步方法. 该方法针对一类不同的混沌系统设计了通用的同步控制器和参数自适应律, 使驱动系统的状态变量和响应系统的状态变量按照给定比例矩阵达到同步, 同步误差按预设的指数速率收敛. 由于比例矩阵和指数速率不为第三方所知, 可提高信息的抗破译能力. 同时, 通过调节相关控制器参数, 可在有限时间内达到投影同步, 并实现对同步时间的有效控制. 数值模拟结果的对比和分析验证了所提方法是有效的和鲁棒的.

关键词:

Abstract

To solve the problem of indeterminate synchronization time in different chaotic systems, this paper presents a time-controllable synchronization scheme. A general synchronization controller and parameter update laws are proposed to stabilize the error system, thus the drive and response systems could be synchronized up to a given scaling matrix at a pre-specified exponential convergence rate. The synchronization time formula is strictly deduced, which suggests that the speed of synchronization is determined by several parameters, such as exponential rate, initial system value and other parameters brought in by the controller. By adjusting these parameters, the performance of the synchronization can be effectively improved. In numerical simulation, two nonidentical 3D autonomous chaotic systems are chosen to verify this method. The error system can be rapidly stabilized, and unknown parameters are also identi?ed correctly. Firally, two groups of time-controllable parameters are given to verify the theory, wherein synchronization of both cases can be obtained quickly and each result of the synchronization is consistent with the theoretical calculation. The synchronization scheme is characterized by high safety and efficiency, and has its potential value in secure communication.

Keywords:

作者及机构信息

1.
湖南大学信息科学与工程学院, 长沙 410082

基金项目: 国家自然科学基金(批准号: 61274020)和湖南省高校重点实验室开放基金(批准号: 12K011)资助的课题.

Authors and contacts

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

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 61274020), and the Open Fund Project of Key Laboratory in Hunan Universities, China (Grant No. 12K011).

参考文献

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施引文献

[1]	Pecora L M, Carroll T L 1990 Phys. Rev. Lett. 64 821
[2]	Zhang R X, Tian G, Li P, Yang S P 2008 Acta. Phys. Sin. 57 2073 (in Chinese) [张若洵, 田钢, 栗苹, 杨世平 2008 57 2073]
[3]
[4]
[5]	Li J F, Li N, Liu Y P, Gan Y 2009 Acta. Phys. Sin. 58 0779 (in Chinese) [李建芬, 李农, 刘宇平, 甘轶 2009 58 0779]
[6]
[7]	Wang B, Guan Z H 2010 Nonlinear Anal. RWA 11 1925
[8]
[9]	Zhou P, Wei L J, Cheng X F 2009 Acta. Phys. Sin. 58 5201 (in Chinese) [周平, 危丽佳, 程雪峰 2009 58 5201]
[10]
[11]	Meng J, Wang X Y 2009 Acta. Phys. Sin. 58 0819 (in Chinese) [孟娟, 王兴元 2009 58 0819]
[12]
[13]	Pourmahmood M, Khanmohammadi S, Alizadeh G 2011 Commun Nonlinear Sci Numer. Simulat 16 2853
[14]	Al-Sawalha M M, Noorani M 2010 Commun Nonlinear Sci. Numer Simulat. 15 1036
[15]
[16]	Li X F, Leung A C S, Han X P, Liu X J, Chu Y D 2011 Nonlinear Dynam 63 263
[17]
[18]	Jing X D, Lv L 2008 Acta Phys. Sin. 57 4766 (in Chinese) [敬晓丹, 吕翎 2008 57 4766]
[19]
[20]	Shahverdiev E, Sivaprakasam S, Shore K 2002 Phys. Lett. A 292 320
[21]
[22]
[23]	Guan Z H, Liu Z W, Feng G, Wu Y 2010 IEEE T CircuitsI 57 2182
[24]
[25]	Akcakaya M, Nehorai A 2010 IEEE Trans. Signal Process 58 4994
[26]	Wang Z L, Shi X R 2010 Nonlinear Dynam 59 559
[27]
[28]	Li J F, Li N 2011 Acta. Phys. Sin. 60 080507 (in Chinese) [李建芬, 李农 2011 60 87]
[29]
[30]	Yu Y G, Li H X 2010 Nonlinear Anal. RWA 11 2456
[31]
[32]	Yang W, Sun J T 2010 Phys. Lett. A 374 557
[33]
[34]
[35]	Li S H, Tian Y P 2003 Chaos Soliton. Fract. 15 303
[36]	Vincent U E, Guo R 2011 Phys. Lett. A 375 2322
[37]
[38]	Aghababa M P, Khanmohammadi S, Alizadeh G 2011 Appl. Math. Mode. 35 3080
[39]
[40]
[41]	Yang Y Q, Wu X F 2012 Nonlinear Dynam. 70 197
[42]	Wang H, Han Z Z, Xie Q Y Zhang W 2009 Commun. Nonlinear Sci Numer. Simulat. 14 2239
[43]
[44]	Hou Y Y, Wan Z L, Liao T L 2012 Nonlinear Dynam. 70 315
[45]
[46]
[47]	Chen Z, Yang Y, Qi Q, Yuan Z 2007 Phys. Lett. A 360 696
[48]
[49]	Li Y X, Tang W K S, Chen G R 2005 Int. J. Bifurcat Chaos 15 3367

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