Equivalent circuit in function and topology to Chua&#8217;s circuit and the design methods of these circuits

Zhang Xin-Guo; Sun Hong-Tao; Zhao Jin-Lan; Liu Ji-Zhao; Ma Yi-De; Han Ting-Wu

doi:10.7498/aps.63.200503

Abstract

The characteristics of classical Chua's circuit variables proposed by Leon O. Chua are the voltage on capacitor, the current in inductor and its normalized equation of state. Based on these characteristics, in this paper, three optimized and scaled circuit design methods are proposed. One is the Chua's circuit with five operational amplifiers used for limiting power amplitude for integration. The other two are Chua's function equivalent circuits with nonlinear diode for cellular neural network system integration. At the same time, an optimized cubic form of Chua's diffeomorphism circuit is given. The methods of designing these circuits are applicable to the cubic random circuits dominated by three broken lines. The universality and practical application of design method are demonstrated in the experiment on chaos secure communication.

Keywords:

Authors and contacts

1.
Department of Information Engineering, Shandong Foreign Language Vocational College, Rizhao 276826, China;
2.
School of Information Science and Engineeing, Lanzhou University, Lanzhou 730000, China;
3.
College of Science, Shandong Univertity of Science and Technology, Qingdao 266590, China
Funds: Project supported by the Higher Educational Science and Technology Program of Shandong Province, China (Grant No. J12LN95) and the Natural Science Foundation of Gansu Province, China (Grant No. 3ZS041-A25-017).

References

[1]	Chua L O, Komuro M, Takashi M 1986 IEEE CAS 33 1073
[2]	Chua L O, Lin G N 1990 IEEE CAS 37 885
[3]	Zhang X G, Ma Y D, Li S L 2011 Nonlinear Circuit–Based Analysis and Design (Vol.1) (Beijing: Higher Education Press) pp124-142 (in Chinese) [张新国, 马义德, 李守亮 2011 非线性电路——基础分析与设计(北京: 高等教育出版社) 第124–142页]
[4]	Xu C F, Yan J C, Wang J S, Han T W, Zhang X G 2010 Public Commun. Sci. Technol. 29 86 (in Chinese) [许崇芳, 严纪丛, 王金双, 韩廷武, 张新国 2010 科技传播 29 86]
[5]	Liu C X, Liu T, Liu L, Liu K 2004 Soliton. Fract. 22 1031
[6]	Zhang X G, Cui H X, Yu R P, Li Y, Zhang X Q, Wei M S 2010 J. Qufu Normal Univ. 36 91 (in Chinese) [张新国, 崔红霞, 于瑞萍, 李娅, 张兴芹, 魏曼莎 2010 曲阜师范大学学报 (自然科学版) 36 91]
[7]	Zhang X G, Yan J C, Xu C F, Cui H X, Yu R P 2011 J. Qufu Normal Univ. 37 50 (in Chinese) [张新国, 严纪丛, 许崇芳, 崔红霞, 于瑞萍 2011 曲阜师范大学学报 (自然科学版) 37 50]
[8]	Lu Y Y, Xue L P 2003 J. Electr. Electron. Education 25 67 (in Chinese) [卢元元, 薛丽萍 2003 电气电子教学学报 25 67]
[9]	Shao S Y, Min F H, Wu X H, Zhang X G 2014 Acta Phys. Sin. 63 060501 (in Chinese) [邵书义, 闵富红, 吴薛红, 张新国 2014 物理学报 63 060501]
[10]	Wang G H, Li Yan 2004 J. Air Force Engineer. Univ. (Natural Science Edition) 5 56 (in Chinese) [王国红, 李彦 2004 空军工程大学学报 5 56]
[11]	Li Z B, Huang J, Huang L, Wang M Z, Yao Y F 2014 J. Xuzhou Instit. Technol. (Natural Sciences Edition) 29 36 (in Chinese) [李泽彬, 黄济, 黄雷, 汪明珠, 姚有峰 2014 徐州工程学院学报 (自然科学版) 29 36]
[12]	Shao S Y, Min F H, Wang E R 2012 J. Nanjing Normal Univ. (Engineering and Technology) 12 6 (in Chinese) [绍书义, 闵富红, 王恩荣 2012 南京师范大学学报 (工程技术版) 12 6]
[13]	Zhang X G, Xu C F, Wang J S, Yan J C, Han T W 2010 J. Shandong Univ. (Engineering Science) 40 134 (in Chinese) [张新国, 许崇芳, 王金双, 严纪丛, 韩廷武 2010 山东大学学报 (工学版) 40 134]
[14]	Zhang X G, Zhang J F, Shi S J 2008 Chinese Patent ZL200810129216.2 [张新国, 张剑锋, 史书军 2008 中国专利 ZL200810129216.2]
[15]	Chua L O 1992 Archiv Elektronik bertra-Gungstechnik 46 250
[16]	Fortuna L, Frasca M, Xibilia M G 2009 Chua's Circuit Implementations: Yesterday, Today and Tomorrow (Singapore: World Scientific)
[17]	Chua L O, Yang L 1988 IEEE Trans. Circ. Syst. 35 1257
[18]	He Z Y, Zhang Y F, Lu H T 1999 J. Commun. 20 59 (in Chinese) [何振亚, 张毅峰, 卢洪涛 1999 通信学报 20 59]
[19]	Yang Z M, Xiong L, Zhang X G, Zhang J, Ren W J 2010 J. Northwest Normal Univ. (Natural Science) 46 40 (in Chinese) [杨志民, 熊丽, 张新国, 张洁, 任文娟 2010 西北师范大学学报 (自然科学版) 46 40]
[20]	Yin Y Z 1998 J. Electon. 20 93 (in Chinese) [尹元昭 1998 电子科学学刊 20 93]
[21]	Yin Y Z 1997 Chinese Patent 97112067.6 (in Chinese) [尹元昭 1997 中国专利 97112067.6]
[22]	Zhang X G, Shi S J, Zhang J F 2008 Chinese Patent ZL200810129217.7 (in Chinese) [张新国, 史书军, 张剑锋 2008 中国专利 ZL200810129217.7]
[23]	Guan X P, Fan Z P, Chen C L, Hua C C 2002 Chaos Control and Its Application in Secret Communication (Beijing: National Defence Industry Press) p341 (in Chinese) [关新平, 范正平, 陈彩莲, 华长春 2002 混沌控制及其在保密通信中的应用 (北京: 国防工业出版社) 第341页]

Cited By

[1]	Chua L O, Komuro M, Takashi M 1986 IEEE CAS 33 1073
[2]	Chua L O, Lin G N 1990 IEEE CAS 37 885
[3]	Zhang X G, Ma Y D, Li S L 2011 Nonlinear Circuit–Based Analysis and Design (Vol.1) (Beijing: Higher Education Press) pp124-142 (in Chinese) [张新国, 马义德, 李守亮 2011 非线性电路——基础分析与设计(北京: 高等教育出版社) 第124–142页]
[4]	Xu C F, Yan J C, Wang J S, Han T W, Zhang X G 2010 Public Commun. Sci. Technol. 29 86 (in Chinese) [许崇芳, 严纪丛, 王金双, 韩廷武, 张新国 2010 科技传播 29 86]
[5]	Liu C X, Liu T, Liu L, Liu K 2004 Soliton. Fract. 22 1031
[6]	Zhang X G, Cui H X, Yu R P, Li Y, Zhang X Q, Wei M S 2010 J. Qufu Normal Univ. 36 91 (in Chinese) [张新国, 崔红霞, 于瑞萍, 李娅, 张兴芹, 魏曼莎 2010 曲阜师范大学学报 (自然科学版) 36 91]
[7]	Zhang X G, Yan J C, Xu C F, Cui H X, Yu R P 2011 J. Qufu Normal Univ. 37 50 (in Chinese) [张新国, 严纪丛, 许崇芳, 崔红霞, 于瑞萍 2011 曲阜师范大学学报 (自然科学版) 37 50]
[8]	Lu Y Y, Xue L P 2003 J. Electr. Electron. Education 25 67 (in Chinese) [卢元元, 薛丽萍 2003 电气电子教学学报 25 67]
[9]	Shao S Y, Min F H, Wu X H, Zhang X G 2014 Acta Phys. Sin. 63 060501 (in Chinese) [邵书义, 闵富红, 吴薛红, 张新国 2014 物理学报 63 060501]
[10]	Wang G H, Li Yan 2004 J. Air Force Engineer. Univ. (Natural Science Edition) 5 56 (in Chinese) [王国红, 李彦 2004 空军工程大学学报 5 56]
[11]	Li Z B, Huang J, Huang L, Wang M Z, Yao Y F 2014 J. Xuzhou Instit. Technol. (Natural Sciences Edition) 29 36 (in Chinese) [李泽彬, 黄济, 黄雷, 汪明珠, 姚有峰 2014 徐州工程学院学报 (自然科学版) 29 36]
[12]	Shao S Y, Min F H, Wang E R 2012 J. Nanjing Normal Univ. (Engineering and Technology) 12 6 (in Chinese) [绍书义, 闵富红, 王恩荣 2012 南京师范大学学报 (工程技术版) 12 6]
[13]	Zhang X G, Xu C F, Wang J S, Yan J C, Han T W 2010 J. Shandong Univ. (Engineering Science) 40 134 (in Chinese) [张新国, 许崇芳, 王金双, 严纪丛, 韩廷武 2010 山东大学学报 (工学版) 40 134]
[14]	Zhang X G, Zhang J F, Shi S J 2008 Chinese Patent ZL200810129216.2 [张新国, 张剑锋, 史书军 2008 中国专利 ZL200810129216.2]
[15]	Chua L O 1992 Archiv Elektronik bertra-Gungstechnik 46 250
[16]	Fortuna L, Frasca M, Xibilia M G 2009 Chua's Circuit Implementations: Yesterday, Today and Tomorrow (Singapore: World Scientific)
[17]	Chua L O, Yang L 1988 IEEE Trans. Circ. Syst. 35 1257
[18]	He Z Y, Zhang Y F, Lu H T 1999 J. Commun. 20 59 (in Chinese) [何振亚, 张毅峰, 卢洪涛 1999 通信学报 20 59]
[19]	Yang Z M, Xiong L, Zhang X G, Zhang J, Ren W J 2010 J. Northwest Normal Univ. (Natural Science) 46 40 (in Chinese) [杨志民, 熊丽, 张新国, 张洁, 任文娟 2010 西北师范大学学报 (自然科学版) 46 40]
[20]	Yin Y Z 1998 J. Electon. 20 93 (in Chinese) [尹元昭 1998 电子科学学刊 20 93]
[21]	Yin Y Z 1997 Chinese Patent 97112067.6 (in Chinese) [尹元昭 1997 中国专利 97112067.6]
[22]	Zhang X G, Shi S J, Zhang J F 2008 Chinese Patent ZL200810129217.7 (in Chinese) [张新国, 史书军, 张剑锋 2008 中国专利 ZL200810129217.7]
[23]	Guan X P, Fan Z P, Chen C L, Hua C C 2002 Chaos Control and Its Application in Secret Communication (Beijing: National Defence Industry Press) p341 (in Chinese) [关新平, 范正平, 陈彩莲, 华长春 2002 混沌控制及其在保密通信中的应用 (北京: 国防工业出版社) 第341页]

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Vol. 63, Issue 20 - 2014-10-20

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Equivalent circuit in function and topology to Chua’s circuit and the design methods of these circuits

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Equivalent circuit in function and topology to Chua’s circuit and the design methods of these circuits

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