基于Chua电路的四维超混沌忆阻电路

杨芳艳; 冷家丽; 李清都

doi:10.7498/aps.63.080502

摘要

近年来，忆阻混沌电路受到国内外学者的广泛关注，然而目前四维忆阻系统往往只存在普通混沌（仅有一个正Lyapunov指数）. 本文通过用忆阻替换Chua电路中电阻的新途径，得出一个简单的四维忆阻电路. 与仅含有限个孤立不稳定平衡点的大多已知系统不同，本系统存在无穷多个稳定和不稳定平衡点. 研究发现该系统存在着极限环、混沌、超混沌等丰富的复杂行为. 通过进一步数值分析和电路仿真实验，证实了超混沌吸引子的存在，从而解决了关于四维忆阻电路是否存在超混沌的疑问.

关键词:

混沌 /
忆阻器 /
超混沌 /
Chua电路

Abstract

Recently, there has been a growing interest in chaotic memristive circuits. However, four-dimensional (4D) memristive system often can only exhibit common chaos with only one positive Lyapunov exponent. By replacing the resistor of Chua’s circuit with a memristor, we propose a new simple 4D memristive circuit in this paper. A major difference between our proposed system and the known chaotic or hyperchaotic system is that our modified system has infinitely many stable and unstable equilibria. We show that the system can exhibit rich complex dynamic behaviors, such as limit cycles, chaos and hyperchaos. Further numerical study and circuit simulation verify the existence of a hyperchaotic attractor in the memristive circuit, which gives a positive answer about whether there exists hyperchaos in 4D memristive systems.

Keywords:

chaos /
memristor /
hyperchaos /
Chua’

作者及机构信息

1.
重庆邮电大学, 工业物联网与网络化控制教育部重点实验室, 重庆 400065;

2.
重庆邮电大学非线性电路与系统研究所, 重庆 400065

基金项目: 国家自然科学基金（批准号：61104150）、重庆市杰出青年科学基金（批准号：cstc2013jcyjjq40001）和重庆市自然科学基金（批准号：CSTC2012jjB40009）资助的课题.

Authors and contacts

1.
Key Laboratory of Industrial Internet of Things and Networked Control, Ministry of Education, Chongqing University of Posts and Telecommunications, Chongqing 400065, China;

2.
Institute for Nonlinear Circuits and Systems of Chongqing University of Posts and Telecommunications, Chongqing 400065, China

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 61104150), the Science Fund for Distinguished Young Scholars of Chongqing, China (Grant No. cstc2013jcyjjq40001), and Natural Science Foundation Chongqing, China (Grant No. CSTC2012jjB40009).

参考文献

[1]	Chua L O 1971 IEEE Trans. Circ. Theory 18 507
[2]	Strukov D B, Snider G S, Stewart G R, Williams R S 2008 Nature 453 80
[3]	Tour J M, Tao H 2008 Nature 453 42
[4]	Jia L N, Huang A P, Zheng X H, Xiao Z S, Wang M 2012 Acta Phys. Sin. 65 217306 (in Chinese) [贾林楠, 黄安平, 郑晓虎, 肖志松, 王玫 2012 65 217306]
[5]	Yuriy V P, Massimiliano D V 2010 IEEE Trans. Circ. Syst. I 57 1857
[6]	Xia Q F, Robinett W, Cumbie M W, Banerjee N, Cardinali T J, Yang J J, Wu W, Li X M, Tong W M, Strukov D B, Snider G S, Medeiros-Ribeiro G, Williams R S 2009 Nano Lett. 9 3640
[7]	Ventra M D, Pershin Y V, Chua L O 2009 Proc. IEEE 97 1717
[8]	Borghetti J, Li Z Y, Straznicky J, Li X M, Ohlberg D A A, Wu W, Stewart D R, Williams R S 2009 Proc. Natl. Acad. Sci. U.S.A. 106 1699
[9]	Song D H, L M F, Ren X, Li M M, Zu Y X 2012 Acta Phys. Sin. 61 118101 (in Chinese) [宋德华, 吕梦菲, 任翔, 李萌萌, 俎云霄 2012 61 118101]
[10]	Hu F W, Bao B C, Wu H G, Wang C L 2013 Acta Phys. Sin. 62 218401 (in Chinese) [胡丰伟, 包伯成, 武花干, 王春丽 2013 62 218401]
[11]	Hong Q H, Zeng Y C, Li Z J 2013 Acta Phys. Sin. 62 230502 (in Chinese) [洪庆辉, 曾以成, 李志军 2013 62 230502]
[12]	Bao B C, Wang C L, Wu H G, Qiao X H 2014 Acta Phys. Sin. 63 020504 (in Chinese) [包伯成, 春丽, 武花干, 乔晓华 2014 63 020504]
[13]	Xu B R 2013 Acta Phys. Sin. 62 190506 (in Chinese) [许碧荣 2013 62 190506]
[14]	Li Q D, Hu S Y, Tang S, Zeng G 2013 Int. J. Circ. Theor. 10 1912
[15]	Bao B C, Liu Z, Xu J P 2010 Acta Phys. Sin. 59 3785 (in Chinese) [包伯成, 刘中, 徐建平 2010 59 3785]
[16]	Itoh M, Chua L O 2008 Int. J. Bifur. Chaos 18 3183
[17]	Bao B C, Hu W, Xu J P, Liu Z, Zou L 2011 Acta Phys. Sin. 60 120502 (in Chinese) [包伯成, 胡文, 许建平, 刘中, 邹凌 2011 60 120502]
[18]	Bao B C, Xu J P, Zhou G H, Ma Z H, Zou L 2011 Chin. Phys. B 20 120502
[19]	Bao B C, Liu Z, Xu J P 2010 Chin. Phys. B 19 030510
[20]	Muthuswamy B, Kokate P P 2009 IETE Tech. Rev. 26 415
[21]	Buscarino A, Fortuna L, Frasca M, Gambuzza L V, Sciuto G 2011 2011 10th International Symposium on Signals, Circuits and Systems (ISSCS) Iasi, Romania, June 30-Jnhy 1, 2011 p73
[22]	Li Z J, Zeng Y C, Li Z B 2013 Acta Phys. Sin. 63 010502 (in Chinese) [李志军, 曾以成, 李志斌 2013 63 010502]
[23]	Bao B C, Shi G D, Xu J P, Liu Z, Pan S H 2011 Sci. China Tech. Sci. 41 1135 (in Chinese) [包伯成, 史国栋, 许建平, 刘中, 潘赛虎 2011 中国科学: 技术科学 41 1135]
[24]	Qi A X, Pang Z, Wang G 2011 2011 2nd International Conference on Artificial Intelligence, Management Science and Electronic Commerce (AIMSEC) Zhengzhou, China, August 8-10, 2011 p3949
[25]	Fitch A L, Yu D S, Iu H H C, Sreeram V 2012 Int. J. Bifur. Chaos 22 1250133
[26]	Li Z J, Zeng Y C 2013 Chin. Phys. B 22 040502

施引文献

[1]	Chua L O 1971 IEEE Trans. Circ. Theory 18 507
[2]	Strukov D B, Snider G S, Stewart G R, Williams R S 2008 Nature 453 80
[3]	Tour J M, Tao H 2008 Nature 453 42
[4]	Jia L N, Huang A P, Zheng X H, Xiao Z S, Wang M 2012 Acta Phys. Sin. 65 217306 (in Chinese) [贾林楠, 黄安平, 郑晓虎, 肖志松, 王玫 2012 65 217306]
[5]	Yuriy V P, Massimiliano D V 2010 IEEE Trans. Circ. Syst. I 57 1857
[6]	Xia Q F, Robinett W, Cumbie M W, Banerjee N, Cardinali T J, Yang J J, Wu W, Li X M, Tong W M, Strukov D B, Snider G S, Medeiros-Ribeiro G, Williams R S 2009 Nano Lett. 9 3640
[7]	Ventra M D, Pershin Y V, Chua L O 2009 Proc. IEEE 97 1717
[8]	Borghetti J, Li Z Y, Straznicky J, Li X M, Ohlberg D A A, Wu W, Stewart D R, Williams R S 2009 Proc. Natl. Acad. Sci. U.S.A. 106 1699
[9]	Song D H, L M F, Ren X, Li M M, Zu Y X 2012 Acta Phys. Sin. 61 118101 (in Chinese) [宋德华, 吕梦菲, 任翔, 李萌萌, 俎云霄 2012 61 118101]
[10]	Hu F W, Bao B C, Wu H G, Wang C L 2013 Acta Phys. Sin. 62 218401 (in Chinese) [胡丰伟, 包伯成, 武花干, 王春丽 2013 62 218401]
[11]	Hong Q H, Zeng Y C, Li Z J 2013 Acta Phys. Sin. 62 230502 (in Chinese) [洪庆辉, 曾以成, 李志军 2013 62 230502]
[12]	Bao B C, Wang C L, Wu H G, Qiao X H 2014 Acta Phys. Sin. 63 020504 (in Chinese) [包伯成, 春丽, 武花干, 乔晓华 2014 63 020504]
[13]	Xu B R 2013 Acta Phys. Sin. 62 190506 (in Chinese) [许碧荣 2013 62 190506]
[14]	Li Q D, Hu S Y, Tang S, Zeng G 2013 Int. J. Circ. Theor. 10 1912
[15]	Bao B C, Liu Z, Xu J P 2010 Acta Phys. Sin. 59 3785 (in Chinese) [包伯成, 刘中, 徐建平 2010 59 3785]
[16]	Itoh M, Chua L O 2008 Int. J. Bifur. Chaos 18 3183
[17]	Bao B C, Hu W, Xu J P, Liu Z, Zou L 2011 Acta Phys. Sin. 60 120502 (in Chinese) [包伯成, 胡文, 许建平, 刘中, 邹凌 2011 60 120502]
[18]	Bao B C, Xu J P, Zhou G H, Ma Z H, Zou L 2011 Chin. Phys. B 20 120502
[19]	Bao B C, Liu Z, Xu J P 2010 Chin. Phys. B 19 030510
[20]	Muthuswamy B, Kokate P P 2009 IETE Tech. Rev. 26 415
[21]	Buscarino A, Fortuna L, Frasca M, Gambuzza L V, Sciuto G 2011 2011 10th International Symposium on Signals, Circuits and Systems (ISSCS) Iasi, Romania, June 30-Jnhy 1, 2011 p73
[22]	Li Z J, Zeng Y C, Li Z B 2013 Acta Phys. Sin. 63 010502 (in Chinese) [李志军, 曾以成, 李志斌 2013 63 010502]
[23]	Bao B C, Shi G D, Xu J P, Liu Z, Pan S H 2011 Sci. China Tech. Sci. 41 1135 (in Chinese) [包伯成, 史国栋, 许建平, 刘中, 潘赛虎 2011 中国科学: 技术科学 41 1135]
[24]	Qi A X, Pang Z, Wang G 2011 2011 2nd International Conference on Artificial Intelligence, Management Science and Electronic Commerce (AIMSEC) Zhengzhou, China, August 8-10, 2011 p3949
[25]	Fitch A L, Yu D S, Iu H H C, Sreeram V 2012 Int. J. Bifur. Chaos 22 1250133
[26]	Li Z J, Zeng Y C 2013 Chin. Phys. B 22 040502

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