The 4-dimensional hyperchaotic memristive circuit based on Chua&#8217;s circuit

Yang Fang-Yan; Leng Jia-Li; Li Qing-Du

doi:10.7498/aps.63.080502

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’

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).

References

[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 物理学报 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 物理学报 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 物理学报 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 物理学报 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 物理学报 63 020504]
[13]	Xu B R 2013 Acta Phys. Sin. 62 190506 (in Chinese) [许碧荣 2013 物理学报 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 物理学报 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 物理学报 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 物理学报 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

Cited By

[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 物理学报 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 物理学报 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 物理学报 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 物理学报 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 物理学报 63 020504]
[13]	Xu B R 2013 Acta Phys. Sin. 62 190506 (in Chinese) [许碧荣 2013 物理学报 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 物理学报 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 物理学报 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 物理学报 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

[1]	Wu Chao-Jun, Fang Li-Yi, Yang Ning-Ning. Dynamic analysis and experiment of chaotic circuit of non-homogeneous fractional memristor with bias voltage source. Acta Physica Sinica, 2024, 73(1): 010501. doi: 10.7498/aps.73.20231211
[2]	Guo Hui-Meng, Liang Yan, Dong Yu-Jiao, Wang Guang-Yi. Simplification of Chua corsage memristor and hardware implementation of its neuron circuit. Acta Physica Sinica, 2023, 72(7): 070501. doi: 10.7498/aps.72.20222013
[3]	Xiao Li-Quan, Duan Shu-Kai, Wang Li-Dan. Julia fractal based multi-scroll memristive chaotic system. Acta Physica Sinica, 2018, 67(9): 090502. doi: 10.7498/aps.67.20172761
[4]	Yan Deng-Wei, Wang Li-Dan, Duan Shu-Kai. Memristor-based multi-scroll chaotic system and its pulse synchronization control. Acta Physica Sinica, 2018, 67(11): 110502. doi: 10.7498/aps.67.20180025
[5]	Wu Jie-Ning, Wang Li-Dan, Duan Shu-Kai. A memristor-based time-delay chaotic systems and pseudo-random sequence generator. Acta Physica Sinica, 2017, 66(3): 030502. doi: 10.7498/aps.66.030502
[6]	Wang Wei, Zeng Yi-Cheng, Sun Rui-Ting. Research on a six-order chaotic circuit with three memristors. Acta Physica Sinica, 2017, 66(4): 040502. doi: 10.7498/aps.66.040502
[7]	Ruan Jing-Ya, Sun Ke-Hui, Mou Jun. Memristor-based Lorenz hyper-chaotic system and its circuit implementation. Acta Physica Sinica, 2016, 65(19): 190502. doi: 10.7498/aps.65.190502
[8]	Hong Qing-Hui, Li Zhi-Jun, Zeng Jin-Fang, Zeng Yi-Cheng. Design and simulation of a memristor chaotic circuit based on current feedback op amp. Acta Physica Sinica, 2014, 63(18): 180502. doi: 10.7498/aps.63.180502
[9]	Li Zhi-Jun, Zeng Yi-Cheng, Li Zhi-Bin. Memristive chaotic circuit based on modified SC-CNNs. Acta Physica Sinica, 2014, 63(1): 010502. doi: 10.7498/aps.63.010502
[10]	Xu Bi-Rong. A simplest parallel chaotic system of memristor. Acta Physica Sinica, 2013, 62(19): 190506. doi: 10.7498/aps.62.190506
[11]	Bao Bo-Cheng, Hu Wen, Xu Jian-Ping, Liu Zhong, Zou Ling. Analysis and implementation of memristor chaotic circuit. Acta Physica Sinica, 2011, 60(12): 120502. doi: 10.7498/aps.60.120502
[12]	Fu Shi-Hui, Pei Li-Jun. Chaotic synchronization of Chua’s circuits with nonlinear control. Acta Physica Sinica, 2010, 59(9): 5985-5989. doi: 10.7498/aps.59.5985
[13]	Jia Hong-Yan, Chen Zeng-Qiang, Yuan Zhu-Zhi. Generation and circuit implementation of a large range hyper-chaotic system. Acta Physica Sinica, 2009, 58(7): 4469-4476. doi: 10.7498/aps.58.4469
[14]	Li Ya, Zhang Zheng-Ming, Tao Zhi-Jie. A hyperchaotic sixth-order Chua’s circuit and its hardware implementation. Acta Physica Sinica, 2009, 58(10): 6818-6822. doi: 10.7498/aps.58.6818
[15]	Han Min, Niu Zhi-Qiang, Han Bing. A new approach to synchronization between two different chaotic systems with parametric perturbation. Acta Physica Sinica, 2008, 57(11): 6824-6829. doi: 10.7498/aps.57.6824
[16]	Cang Shi-Jian, Chen Zeng-Qiang, Yuan Zhu-Zhi. Analysis and circuit implementation of a new four-dimensional non-autonomous hyper-chaotic system. Acta Physica Sinica, 2008, 57(3): 1493-1501. doi: 10.7498/aps.57.1493
[17]	Yao Li-Na, Gao Jin-Feng, Liao Ni-Huan. Synchronization of a class of chaotic systems using nonlinear observers. Acta Physica Sinica, 2006, 55(1): 35-41. doi: 10.7498/aps.55.35
[18]	Yu Hong-Jie, Liu Yan-Zhu. Synchronization of symmetrically nonlinear-coupled chaotic systems. Acta Physica Sinica, 2005, 54(7): 3029-3033. doi: 10.7498/aps.54.3029
[19]	Zhang Sheng-Hai, YangHua, Qian Xing-Zhong. A method for controlling hyperchaos of Er-doped fiber laser——Nonlinear time-delay feedback modulating-parameter. Acta Physica Sinica, 2004, 53(11): 3706-3709. doi: 10.7498/aps.53.3706
[20]	YUE LI-JUAN, CHEN YAN-YAN, PENG JIAN-HUA. A CIRCUIT EXPERIMENT FOR CONTROLLING HYPERCHAOS BY MEANS OF PROPORTIONAL PERIODIC PULSE PERTURBATION TO THE SYSTEM VARIABLES. Acta Physica Sinica, 2001, 50(11): 2097-2102. doi: 10.7498/aps.50.2097

Catalog

Vol. 63, Issue 8 - 2014-04-20

Metrics

Abstract views: 7168
PDF Downloads: 940
Cited By: 0

姓名
邮箱
手机号码
标题
留言内容
验证码

Search

Article

留言板

The 4-dimensional hyperchaotic memristive circuit based on Chua’s circuit

Abstract

Authors and contacts

References

Cited By

Catalog

Metrics

Authors

Referees

About Journal

About

Search

Article

留言板

The 4-dimensional hyperchaotic memristive circuit based on Chua’s circuit

Abstract

Authors and contacts

References

Cited By

Catalog

Metrics

Publishing process

Authors

Referees

About Journal

About