简化Lorenz多涡卷混沌吸引子的设计与应用

艾星星; 孙克辉; 贺少波; 王会海

doi:10.7498/aps.63.120511

摘要

将简化Lorenz系统线性化成两个线性系统，采用控制方法得到两涡卷混沌系统，通过扩展两涡卷混沌系统的指标2鞍焦点，设计了多涡卷混沌吸引子. 利用相图、分岔图、Poincaré截面和最大Lyapunov 指数等方法，分析了该多涡卷混沌系统的动力学特性. 设计了多涡卷混沌吸引子的模拟电路，并进行了仿真，数值仿真与电路仿真相一致. 将多涡卷混沌系统应用于图像加密，设计了多涡卷混沌与高级加密标准（AES）的改进混合加密算法，并分析了其加密性能. 结果表明，基于多涡卷混沌系统的改进混合加密算法具有更高的安全性.

关键词:

Abstract

Two linear systems are obtained by employing linearization technique in a simplified Lorenz system, and a two-scroll chaotic attractor is generated via the control method. Multi-scroll chaotic attractors are generated by extending the saddle-focus equilibrium points with index 2. Dynamic characteristics of the multi-scroll chaotic system are analyzed by observing the phase diagrams, bifurcation diagrams, Poincaré sections and calculating the largest Lyapunov exponent. A circuit for the multi-scroll attractor is designed and simulated. The numerical simulation result and the circuit simulation result are consistent with each other. To apply the multi-scroll chaotic systems to image encryption, an improved hybrid encryption algorithm is designed based on the multi-scroll chaotic system and advanced encryption standard (AES), and its encryption performances are analyzed. The results show that the improved hybrid encryption has a higher security.

Keywords:

作者及机构信息

1.
中南大学物理与电子学院, 长沙 410083;

2.
新疆大学物理科学与技术学院, 乌鲁木齐 830046

基金项目: 国家自然科学基金（批准号：61161006，61073187）和中央高校基本科研业务费（批准号：72150050650）资助的课题.

Authors and contacts

1.
School of Physics and Electronics, Central South University, Changsha 410083, China;

2.
School of Physics Science and Technology, Xinjiang University, Urumqi 830046, China

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 61161006, 61073187) and the Fundamental Research Fund for the Central Universities, China (Grant No. 72150050650).

参考文献

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[4]	Trejo G R, Tlelo C E, Jimenez F 2012 Commun. Nonlinear Sci. Numerical Simulat. 17 4328
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[8]	Yu S M, L J H, Chen G R 2007 Phys. Lett. A 364 244
[9]	Sanchez-Lopez C 2011 Appl. Math. Computat. 217 4350
[10]	Xu F, Yu P 2010 Math. Anal. Appl. 362 252
[11]	Li G L, Chen X Y 2009 Commun. Nonlinear Sci. Numerical Simul. 14 194
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[13]	Luo X H, Tu Z W, Liu X R, Cai C, Liang Y L, Gong P 2010 Chin. Phys. B 19 070510
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[15]	Xi H L, Yu S M, Zhang Z X 2010 Chaos Fractals Theories and Applictaions, 2010 International Workshop on IEEE Kunming, China, October 29-31, 2010 p92
[16]	Gui Z, Wu X, Chen Y 2013 Int. J. Mod. Phys. B 27 1350007
[17]	Liu X, Shen X, Zhang H 2012 Int. J. Bifurc. Chaos Appl. Sci. Engineer. 22 1250033
[18]	Yu S M, L J H, Chen G R 2011 Circuits and Systems IEEE International Symposium on IEEE Rio de Janeiro, Brazil, May 15-18, 2011 p1335
[19]	Yu S M, Lu J H 2012 Circ. Syst. 59 1015
[20]	Kais B, Abdessattar C, Ahmed T 2011 Chaos Solition. Fract. 44 79
[21]	Lu J H, Yu X H, Chen G R 2003 Circ. Syst. 50 198
[22]	Zhao P T, Liu G, Wang M H, Peng J L 2012 Biomed. Engineer. Inform. 5 186
[23]	Sun K H, He S B, Zhu C X, He Y 2013 Acta Elect. Sin. 9 1765 (in Chinese) [孙克辉, 贺少波, 朱从旭, 何毅 2013 电子学报 9 1765]
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施引文献

[1]	Yu S M 2005 Acta Phys. Sin. 54 1500 (in Chinese) [禹思敏 2005 54 1500]
[2]	Maksuanpan S, San U W 2013 Knowledge and Smart Technology 5 134
[3]	Zhang C X, Yu S M 2009 Acta Phys. Sin. 58 120 (in Chinese) [张朝霞, 禹思敏 2009 58 120]
[4]	Trejo G R, Tlelo C E, Jimenez F 2012 Commun. Nonlinear Sci. Numerical Simulat. 17 4328
[5]	Chen L, Peng H J, Wang D S 2008 Acta Phys. Sin. 57 3337 (in Chinese) [谌龙, 彭海军, 王德石 2008 57 3337]
[6]	Bao B C, Xu Q, Xu Y M, Wang X F 2001 J. Circ. Syst. 16 69 (in Chinese) [包伯成, 徐强, 徐煜明, 汪小锋 2001 电路与系统学报 16 69]
[7]	Mustafa T, Hidayet O 2010 Expert Syst. Appl. 37 8667
[8]	Yu S M, L J H, Chen G R 2007 Phys. Lett. A 364 244
[9]	Sanchez-Lopez C 2011 Appl. Math. Computat. 217 4350
[10]	Xu F, Yu P 2010 Math. Anal. Appl. 362 252
[11]	Li G L, Chen X Y 2009 Commun. Nonlinear Sci. Numerical Simul. 14 194
[12]	Liu C X, Yi J, Xi X C 2012 Proced. Engineer. 29 957
[13]	Luo X H, Tu Z W, Liu X R, Cai C, Liang Y L, Gong P 2010 Chin. Phys. B 19 070510
[14]	Mao W, Guang H, Li L H 2010 Systems and Control in Aeronautics and Astoinautics 3rd International Symposium on IEEE Harbin, China, June 8-10, 2010 p289
[15]	Xi H L, Yu S M, Zhang Z X 2010 Chaos Fractals Theories and Applictaions, 2010 International Workshop on IEEE Kunming, China, October 29-31, 2010 p92
[16]	Gui Z, Wu X, Chen Y 2013 Int. J. Mod. Phys. B 27 1350007
[17]	Liu X, Shen X, Zhang H 2012 Int. J. Bifurc. Chaos Appl. Sci. Engineer. 22 1250033
[18]	Yu S M, L J H, Chen G R 2011 Circuits and Systems IEEE International Symposium on IEEE Rio de Janeiro, Brazil, May 15-18, 2011 p1335
[19]	Yu S M, Lu J H 2012 Circ. Syst. 59 1015
[20]	Kais B, Abdessattar C, Ahmed T 2011 Chaos Solition. Fract. 44 79
[21]	Lu J H, Yu X H, Chen G R 2003 Circ. Syst. 50 198
[22]	Zhao P T, Liu G, Wang M H, Peng J L 2012 Biomed. Engineer. Inform. 5 186
[23]	Sun K H, He S B, Zhu C X, He Y 2013 Acta Elect. Sin. 9 1765 (in Chinese) [孙克辉, 贺少波, 朱从旭, 何毅 2013 电子学报 9 1765]
[24]	Sheng L Y, Xiao Y Y, Sheng Z 2008 Acta Phys. Sin. 57 4007 (in Chinese) [盛利元, 肖燕予, 盛喆 2008 57 4007]
[25]	Wang C L, Wang G Y, Sun Y, Chen W 2011 Proceedings-4th International Workshop on Chaos-Fractals Theories and Applications China, October 19-21, 2011 p183
[26]	Lin Y, Wang C H, Xu H 2012 Acta Phys. Sin. 61 73 (in Chinese) [林愿, 王春华, 徐浩 2012 61 73]
[27]	Sun K H, Sprott J C 2009 Int. J. Bifurc. Chaos 19 1357

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