基于现场可编程逻辑门阵列的新型混沌系统实现

邵书义; 闵富红; 吴薛红; 张新国

doi:10.7498/aps.63.060501

摘要

构建了一个新的五维变形蔡氏系统，通过数值仿真，分析平衡点的稳定性、分岔图和Lyapunov指数谱，研究系统特有的基本非线性动力学行为，还分析了改变不同参数时系统动力学行为的变化. 基于混沌系统的数值仿真分析以及数字化处理技术，将五维变形蔡氏系统状态方程进行离散化处理，并根据IEEE-754标准和模块化设计理念构建出实现混沌系统变量运算关系的基本模块，进一步利用现场可编程逻辑门阵列硬件平台实现了五维变形蔡氏系统的混沌吸引子. 研究结果表明，新五维变形蔡氏系统具有新的混沌动力学行为，并通过硬件证实了新系统的存在性和物理上的可实现性.

关键词:

Abstract

A new five-dimensional modified Chua’s system is proposed and its dynamic properties are investigated through numerical simulations, the stabilization of equilibrium points, bifurcation diagrams, and Lyapunov exponent spectrum. The different dynamic behaviors of the new system are analyzed with system parameters changed. Based on the mathematical model of the new system and the digital processing technology, the five-dimensional modified Chua’s system is discretized. According to IEEE-754 standard and module-based design idea, basic floating-point operational modules are designed. Furthermore, the chaotic attractors of the five-dimensional modified Chua’s system are realized by field programmable gate array. The investigation results show that the chaotic system is different from the existing chaotic systems. It also shows a good agreement between numerical simulation and hardware implementation, which proves the existence and realizability of the new chaotic system.

Keywords:

chaotic system /
dynamical behavior /
field programmable gate array implementation

作者及机构信息

1.
南京师范大学电气与自动化工程学院, 南京 210042;

2.
兰州大学信息科学与工程学院, 兰州 730000

基金项目: 国家自然科学基金（批准号：51075275）、江苏省自然科学基金（批准号：BK20131402）、教育部留学回国人员科研启动基金（批准号：20121707）和江苏省“六大人才”高峰计划资助的课题.

Authors and contacts

1.
School of Electrical and Automation Engineering, Nanjing Normal University, Nanjing 210042, China;

2.
School of Information Science and Engineering, Lanzhou University, Lanzhou 730000, China

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 51075275), the Natural Science Foundation of Jiangsu Province, China (Grant No. BK20131402), the Scientific Research Staring Foundation for the Returned Overseas Chinese Scholars of Ministry of Education, China (Grant No. 20121707), and the "Summit of the Six Top Talents" Program of Jiangsu Province, China.

参考文献

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[2]	Chen G R, Ueta T 1999 Int. J. Bifur. Chaos 9 1465
[3]	L J H, Chen G R 2002 Int. J. Bifur. Chaos 12 659
[4]	Yu F, Wang C H, Yin J W, Xu H 2012 Acta Phys. Sin. 61 020506 (in Chinese) [余飞, 王春华, 尹晋文, 徐浩 2012 61 020506]
[5]	Liu C X, Liu T, Liu L, Liu K 2004 Chaos Solition. Fract. 22 1031
[6]	Luo M W, Luo X H, Li H Q 2013 Acta Phys. Sin. 62 020512 (in Chinese) [罗明伟, 罗小华, 李华青 2013 62 020512]
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[9]	Wang Z, Huang X, Li Y X, Song X N 2013 Chin. Phys. B 22 010504
[10]	Guan Z H, Huang F J, Guan W J 2005 Phys. Lett. A 346 153
[11]	Wang X Y, Luan D P 2013 Commun. Nonlin. Sci. Numer. Simulat. 18 3075
[12]	Jin J 2012 Opt. Lasers Eng. 50 1836
[13]	Zhou X Y 2012 Acta Phys. Sin. 61 030504 (in Chinese) [周小勇 2012 61 030504]
[14]	Li C L, Yu S M, Luo X S 2012 Acta Phys. Sin. 61 110502 (in Chinese) [李春来, 禹思敏, 罗晓曙 2012 61 110502]
[15]	Feng C W, Cai L, Kang Q, Zhang L S 2011 Acta Phys. Sin. 60 030503 (in Chinese) [冯朝文, 蔡理, 康强, 张立森 2011 60 030503]
[16]	Wang G Y, Qiu S S, Li H W, Li C F, Zheng Y 2006 Chin. Phys. 15 2872
[17]	Kim D, Chang P H, Kim S H 2013 Nonlin. Dyn. 73 1883
[18]	Abooee A, Yaghini-Bonabi H A, Jahed-Motlagh M R 2013 Commun. Nonlin. Sci. Numer. Simulat. 18 1235
[19]	Liu Q, Fang J Q, Zhao G, Li Y 2012 Acta Phys. Sin. 61 130508 (in Chinese) [刘强, 方锦清, 赵耿, 李永 2012 61 130508]
[20]	Azzaz M S, Tanougast C, Sadoudi S, Fellah R, Dandache A 2013 Commun. Nonlinear Sci. Numer. Simulat. 18 1792
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[23]	Wang G Y, Bao X L, Wang Z L 2008 Chin. Phys. B 17 3596
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施引文献

[1]	Chen G, Dong X 1998 From Chaos to Order: Methodologies, Perspectives and Applications (Singapore: World Scientific)
[2]	Chen G R, Ueta T 1999 Int. J. Bifur. Chaos 9 1465
[3]	L J H, Chen G R 2002 Int. J. Bifur. Chaos 12 659
[4]	Yu F, Wang C H, Yin J W, Xu H 2012 Acta Phys. Sin. 61 020506 (in Chinese) [余飞, 王春华, 尹晋文, 徐浩 2012 61 020506]
[5]	Liu C X, Liu T, Liu L, Liu K 2004 Chaos Solition. Fract. 22 1031
[6]	Luo M W, Luo X H, Li H Q 2013 Acta Phys. Sin. 62 020512 (in Chinese) [罗明伟, 罗小华, 李华青 2013 62 020512]
[7]	Shao S Y, Min F H, Ma M L, Wang E R 2013 Acta Phys. Sin. 62 130504 (in Chinese) [邵书义, 闵富红, 马美玲, 王恩荣 2013 62 130504]
[8]	Hua C C, Yang B, Ouyang G X, Guan X P 2005 Phys. Lett. A 342 305
[9]	Wang Z, Huang X, Li Y X, Song X N 2013 Chin. Phys. B 22 010504
[10]	Guan Z H, Huang F J, Guan W J 2005 Phys. Lett. A 346 153
[11]	Wang X Y, Luan D P 2013 Commun. Nonlin. Sci. Numer. Simulat. 18 3075
[12]	Jin J 2012 Opt. Lasers Eng. 50 1836
[13]	Zhou X Y 2012 Acta Phys. Sin. 61 030504 (in Chinese) [周小勇 2012 61 030504]
[14]	Li C L, Yu S M, Luo X S 2012 Acta Phys. Sin. 61 110502 (in Chinese) [李春来, 禹思敏, 罗晓曙 2012 61 110502]
[15]	Feng C W, Cai L, Kang Q, Zhang L S 2011 Acta Phys. Sin. 60 030503 (in Chinese) [冯朝文, 蔡理, 康强, 张立森 2011 60 030503]
[16]	Wang G Y, Qiu S S, Li H W, Li C F, Zheng Y 2006 Chin. Phys. 15 2872
[17]	Kim D, Chang P H, Kim S H 2013 Nonlin. Dyn. 73 1883
[18]	Abooee A, Yaghini-Bonabi H A, Jahed-Motlagh M R 2013 Commun. Nonlin. Sci. Numer. Simulat. 18 1235
[19]	Liu Q, Fang J Q, Zhao G, Li Y 2012 Acta Phys. Sin. 61 130508 (in Chinese) [刘强, 方锦清, 赵耿, 李永 2012 61 130508]
[20]	Azzaz M S, Tanougast C, Sadoudi S, Fellah R, Dandache A 2013 Commun. Nonlinear Sci. Numer. Simulat. 18 1792
[21]	Wang Z L 2008 Comput. Eng. Appl. 44 84 (in Chinese) [王忠林 2008 计算机工程与应用 44 84]
[22]	Wang Z L, Wang G Y 2009 Comput. Eng. Des. 30 3365 (in Chinese) [王忠林, 王光义 2009 计算机工程与设计 30 3365]
[23]	Wang G Y, Bao X L, Wang Z L 2008 Chin. Phys. B 17 3596
[24]	Zhou W J, Yu S M 2009 Acta Phys. Sin. 58 113 (in Chinese) [周武杰, 禹思敏 2009 58 113]
[25]	Zhou W J, Yu S M 2008 Acta Phys. Sin. 57 4738 (in Chinese) [周武杰, 禹思敏 2008 57 4738]
[26]	Yin Y Z 1996 Int. J. Bifurc. Chaos 6 2101

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