混沌相空间转动同步及判别切换保密通信的研究

doi:10.11959/j.issn.1000-436x.2016201

摘要/Abstract

摘要：

研究了一个新的混沌动力系统，进行了动力学分析，通过对平衡点、Lyapunov 指数、Lyapunov 维数和Poincare截面的研究，证实了系统的混沌行为。对混沌系统的相空间Z轴转动进行了研究，引入了转动矩阵，建立了相空间内的Z轴转动模型，并进行了混沌系统空间转动同步研究。利用上述研究成果，提出了混沌判别切换保密通信系统的方案，适合应用于信息安全通信中。

关键词: 混沌, 混沌同步, 混沌吸引子, 保密通信

Abstract:

A new chaotic dynamic system was proposed and the dynamic of this system was analyzed.Through the research of balance point,Lyapunov index,Lyapunov dimension and Poincare section,the chaotic behavior of the system was approved.Z axis of chaos system phase space was researched.Z axis rotation model in the phase space was built through introducing rotation matrix,and chaos system space synchronous rotation was researched.Based on the research results above,a chaotic distinguish switching security communication system was presented for the communication of information security.

Key words: chaos, chaos synchronization, chaotic attractor, security communication

孙广明,黄金杰. 混沌相空间转动同步及判别切换保密通信的研究[J]. 通信学报, 2016, 37(10): 99-107.

Guang-ming SUN,Jin-jie HUANG. Study on chaos phase space synchronous rotation and distinguish switching security communication[J]. Journal on Communications, 2016, 37(10): 99-107.

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参考文献 21

[1]	王斌, 吴超, 朱德兰 . 一个新的分数阶混沌系统的翼倍增及滑模同步[J]. 物理学报, 2013,62(23):230506. WANG B , WU C , ZHU D L . A new double-wing fractional-order chaotic system and its synchronization by sliding mode[J]. Acta Phys Sin, 2013,62(23):230506.
[2]	LIU C , LIU L , LIU T . A novel three-dimensional autonomous chaos system[J]. Chaos Solitons ＆Fractals, 2009,39(4): 1950-1958.
[3]	周欣, 王春华, 郭小蓉 . 一个新的网格多翅膀混沌系统及电路实现[J]. 物理学报, 2012,61(20):200506. ZHOU X , WANG C H , GUO X R . A new grid multi-wing chaotic system and its circuit implementatic[J]. Acta Phys Sin, 2012,61(20):200506.
[4]	黄丽莲, 辛方, 王霖郁 . 新分数阶混沌系统的异结构同步及其电路仿真[J]. 系统仿真学报, 2012,24(7): 1479-1483. HUANG L L , XIN F , WANG L Y . Circuit simulation and synchronization of new fractional-order chaotic system[J]. Journal of System simulation, 2012,24(7): 1479-1483.
[5]	PECORA L M , CARROLL T L . Synchronization in chaos systems[J]. Phys Rev Let, 1990,64(8): 821-824.
[6]	于娜, 丁群, 陈红 . 异结构系统混沌同步及其在保密通信中的应用[J]. 通信学报, 2007,28(10): 73-78. YU N , DING Q , CHEN H . Synchronization of different structure chaotic systems and the application in secure communication[J]. Journal on Communications, 2007,28(10): 73-78.
[7]	PECORA L M , CARROLL T L . Driving system with chaotic signals[J]. Phys Rev , 1991,44(2): 374-383.
[8]	李国辉, 周世平, 徐德明 . 用主动被动分拆法和主动-间隙有何研究Henon映射的混沌同步[J]. 量子电子学报, 2001,18(2): 167-171. LI G H , ZHOU S P , XU D M . Synchronizing henon mapping via active-passive decomposition and active-occasional coupling[J]. Chinese Journal of Quantum Electronics, 2001,18(2): 167-171.
[9]	CHRN G R , LAI D J . Making a dynamical system chaotic:feedback control of Lyapunov exponents for discrete time dynamical systems[J]. IEEE Trans on Circuit and System-I 1997,44:250.
[10]	GUEMEZ J , MATIAS M A . Control chaos in unidimensional[J]. Phys Lett,1993,A181:29.
[11]	刘恒, 李生刚, 孙业国 ,等. 带有未知非对称控制增益的不确定分数阶混沌系统自适应模糊同步控制[J]. 物理学报, 2015,64(7):070503. LIU H , LI S G , SUN Y G ,et al. Adaptive fuzzy synchronization for uncertain fractional-order chaotic systems with unknown nonsymmetrical control gain[J]. Acta Phys Sin, 2015,64(7):070503.
[12]	HWANG E J , HYUN C H , KIM E ,et al. Fuzzy model based adaptive synchronization of uncertain chaotic systems:robust tracking control approach[J]. Physics Letters A, 2009,373: 1935-1939.
[13]	VASSILIS K , ILIAS P , JOHN N L . Intelligent classification using adaptive fuzzy logic systems[C]// Proc of the 4th Int IEEE Conf on Intelligent Systems. Varna,IEEE, 2008: 8-13.
[14]	AGHABABA M P . Finite-time chaos control and synchronization of fractional-order nonautonomous chaotic (hyper- chaotic) systems using fractional nonsingular terminal sliding mode technique[J]. Nonlinear Dynamics, 2012,69(1-2): 247-261.
[15]	PAI M C . Robust synchronization of chaotic systems using adaptive sliding mode output feedback control[J]. Proceedings of the Institution of Mechanical Engineers Part I:Journal of Systems and Control Engineering, 2012,226(5): 598-605.
[16]	杨涛, 邵惠鹤 . 基于遗传算法混沌系统同步的研究[J]. 控制理论与应用, 2002,10(5): 789-793. YANG T , SHAO H H . Chaotic synchronization based on genetic algorithms[J]. Control Theory and Applications, 2002,10(5): 789-793.
[17]	MEI R , WU Q X , JIANG C S . Robust adaptive backstepping control for a class of uncertain nonlinear systems based on disturbance observers[J]. Science China-Information Science, 2010,53(6): 1201-1215.
[18]	张友安, 余名哲, 耿宝亮 . 基于投影法的不确定分数阶混沌系统自适应同步[J]. 电子与信息学报, 2015,37(2): 455-460. ZHANG Y A , YU M Z , GENG B L . Adaptive synchronization of uncertain fractional-order chaotic systems based on projective method[J]. Journal of Electronics ＆ Information Technology, 2015,37(2): 455-460
[19]	王平立, 宋斌, 王玲 . 混沌时间序列的Kolmogorov熵的应用研究[J]. 计算机工程与应用, 2006,21: 162-164. WANG P L , SONG B , WANG L . Study on Kolmogorov entropy based on chaotic time series[J]. Computer Engineering Applications, 2006,21: 162-164.
[20]	STEVEN M,PRINNCUS . Approximate entropy as a measure of system complexity[J]. Proceedings of the National Academy of Sciences of USA, 1991,88(3): 2297-2301.
[21]	赵贵兵, 石炎福, 段文锋 ,等. 从混沌时间序列同时计算关联维和Kolmogorov 熵[J]. 计算物理, 1999,16(5): 309-315. ZHAO G B , SHI Y F , DUAN W F ,et al. Computing fractal dimension and time series[J]. Chinese Journal of Computational Physics, 1999,16(5): 309-315.