Design and multistability analysis of five-value memristor-based chaotic system with hidden attractors

doi:10.1088/1674-1056/ac1e13

中国物理B ›› 2021, Vol. 30 ›› Issue (10): 100506-100506.doi: 10.1088/1674-1056/ac1e13

Design and multistability analysis of five-value memristor-based chaotic system with hidden attractors

Li-Lian Huang(黄丽莲)^1,2, Shuai Liu(刘帅)^1,2, Jian-Hong Xiang(项建弘)^1,2,†, and Lin-Yu Wang(王霖郁)^1,2

1 College of Information and Communication Engineering, Harbin Engineering University, Harbin 150001, China;
2 MIIT Key Laboratory of Advanced Marine Communication and Information Technology, Harbin 150001, China

收稿日期:2021-05-09 修回日期:2021-07-19 接受日期:2021-08-17 出版日期:2021-09-17 发布日期:2021-10-08
通讯作者: Jian-Hong Xiang E-mail:xiangjianhong@hrbeu.edu.cn
基金资助:
Project supported by the National Natural Science Foundation of China (Grant No. 61203004), the Natural Science Foundation of Heilongjiang Province, China (Grant No. F201220), and the Heilongjiang Provincial Natural Science Foundation of Joint Guidance Project (Grant No. LH2020F022).

Design and multistability analysis of five-value memristor-based chaotic system with hidden attractors

Li-Lian Huang(黄丽莲)^1,2, Shuai Liu(刘帅)^1,2, Jian-Hong Xiang(项建弘)^1,2,†, and Lin-Yu Wang(王霖郁)^1,2

1 College of Information and Communication Engineering, Harbin Engineering University, Harbin 150001, China;
2 MIIT Key Laboratory of Advanced Marine Communication and Information Technology, Harbin 150001, China

Received:2021-05-09 Revised:2021-07-19 Accepted:2021-08-17 Online:2021-09-17 Published:2021-10-08
Contact: Jian-Hong Xiang E-mail:xiangjianhong@hrbeu.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Grant No. 61203004), the Natural Science Foundation of Heilongjiang Province, China (Grant No. F201220), and the Heilongjiang Provincial Natural Science Foundation of Joint Guidance Project (Grant No. LH2020F022).

摘要/Abstract

摘要： A five-value memristor model is proposed, it is proved that the model has a typical hysteresis loop by analyzing the relationship between voltage and current. Then, based on the classical Liu-Chen system, a new memristor-based four-dimensional (4D) chaotic system is designed by using the five-value memristor. The trajectory phase diagram, Poincare mapping, bifurcation diagram, and Lyapunov exponent spectrum are drawn by numerical simulation. It is found that, in addition to the general chaos characteristics, the system has some special phenomena, such as hidden homogenous multistabilities, hidden heterogeneous multistabilities, and hidden super-multistabilities. Finally, according to the dimensionless equation of the system, the circuit model of the system is built and simulated. The results are consistent with the numerical simulation results, which proves the physical realizability of the five-value memristor-based chaotic system proposed in this paper.

关键词: five-valued memristor, chaotic system, hidden attractor, multistability

Abstract: A five-value memristor model is proposed, it is proved that the model has a typical hysteresis loop by analyzing the relationship between voltage and current. Then, based on the classical Liu-Chen system, a new memristor-based four-dimensional (4D) chaotic system is designed by using the five-value memristor. The trajectory phase diagram, Poincare mapping, bifurcation diagram, and Lyapunov exponent spectrum are drawn by numerical simulation. It is found that, in addition to the general chaos characteristics, the system has some special phenomena, such as hidden homogenous multistabilities, hidden heterogeneous multistabilities, and hidden super-multistabilities. Finally, according to the dimensionless equation of the system, the circuit model of the system is built and simulated. The results are consistent with the numerical simulation results, which proves the physical realizability of the five-value memristor-based chaotic system proposed in this paper.

Key words: five-valued memristor, chaotic system, hidden attractor, multistability

中图分类号: (Nonlinear dynamics and chaos)

05.45.-a

05.45.Pq (Numerical simulations of chaotic systems)

Li-Lian Huang(黄丽莲), Shuai Liu(刘帅), Jian-Hong Xiang(项建弘), and Lin-Yu Wang(王霖郁). Design and multistability analysis of five-value memristor-based chaotic system with hidden attractors[J]. 中国物理B, 2021, 30(10): 100506-100506.

参考文献

[1] Chua L O 1971 IEEE Trans. Circ. Theory 18 507
[2] Chua L O and Kang S M 1976 Proc. IEEE 64 209
[3] Strukov D B, Snider G S, Stewart D R and Williams R S 2008 Nature 453 80
[4] Itoh M and Chua L O 2008 Int. J. Bifurc. Chaos 18 3183
[5] Bao B C, Xu J P and Liu Z 2010 Chin. Phys. Lett. 27 070504
[6] Bao B C, Xu J P, Zhou G H, Ma Z H and Zou L 2011 Chin. Phys. B 20 120502
[7] Bao B C, Liu Z and Xu J P 2010 Chin. Phys. B 19 030510
[8] Muthuswamy B 2010 Int. J. Bifurc. Chaos 20 1335
[9] Liu G Z, Zheng L J, Wang G Y, Shen Y R and Liang Y 2019 IEEE Access 7 43691
[10] Chen C J, Chen J Q, Bao H, Chen M and Bao B C 2019 Nonlinear Dyn. 95 3385
[11] Ying J J, Wang G Y, Dong Y J and Yu S M 2019 Int. J. Bifurc. Chaos 29 1930030
[12] Chen J J, Yan D W, Duan S K and Wang L D 2020 Chin. Phys. B 29 110504
[13] Muthuswamy B and Kokate P P 2009 IETE Tech. Rev. 26 417
[14] Xi H L, Li Y X and Huang X 2014 Entropy 16 6240
[15] Bao B C, Jiang T, Xu Q, Chen M, Wu H G and Hu Y H 2016 Nonlinear Dyn. 86 1711
[16] Wang G Y, Yuan F, Chen G R 2018 Chaos 28 013125
[17] Zhou W, Wang G Y, Shen Y R 2018 Int. J. Bifurc. Chaos 28 1830033
[18] Zhang X, Wang C H. 2019 Int. J. Bifurc. Chaos 29 1950117
[19] Deng Q L, Wang C H and Yang L M 2020 Int. J. Bifurc. Chaos 30 2050086
[20] Yan B, He S B and Wang S J 2020 Math. Probl. Eng. 2020 2468134
[21] Gu S Q, He S B, Wang H H and Du B X 2021 Chaos, Solitons, and Fractals 143 110613
[22] Wang X Y, Zhang X and Gao M 2020 Complexity 2020 6949703
[23] Huang L L, Yao W J, Xiang J H and Zhang Z F 2020 Complexity 2020 2408460
[24] Chua L O 2011 Appl. Phys. A 102 765
[25] Chua L O 2012 Proc. IEEE 100 1920
[26] Adhikari S P, Sah M P, Kim H and Chua L O 2013 IEEE Trans. Circ. Syst. I: Reg. Papers 60 3008
[27] Liu W B and Chen G R 2003 Int. J. Bifurc. Chaos 13 261
[28] Liu W B and Chen G R 2004 Int. J. Bifurc. Chaos 14 1395
[29] Khan A and Singh S 2018 Chin. J. Phys. 56 238
[30] Gottwald G A and Melbourne I 2004 Proc. Math. Phys. Eng. Sci. 460 603

Design and multistability analysis of five-value memristor-based chaotic system with hidden attractors

Design and multistability analysis of five-value memristor-based chaotic system with hidden attractors

RichHTML

PDF (PC)

赞

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 15

Metrics

本文评价

推荐阅读 0

[1]	Xiaodong Jiao(焦晓东), Mingfeng Yuan(袁明峰), Jin Tao(陶金), Hao Sun(孙昊), Qinglin Sun(孙青林), and Zengqiang Chen(陈增强). Memristor hyperchaos in a generalized Kolmogorov-type system with extreme multistability[J]. 中国物理B, 2023, 32(1): 10507-010507.
[2]	Fangfang Zhang(张芳芳), Zhe Huang(黄哲), Lei Kou(寇磊), Yang Li(李扬), Maoyong Cao(曹茂永), and Fengying Ma(马凤英). Data encryption based on a 9D complex chaotic system with quaternion for smart grid[J]. 中国物理B, 2023, 32(1): 10502-010502.
[3]	Rui Wang(王蕊), Meng-Yang Li(李孟洋), and Hai-Jun Luo(罗海军). Exponential sine chaotification model for enhancing chaos and its hardware implementation[J]. 中国物理B, 2022, 31(8): 80508-080508.
[4]	Shaobo He(贺少波), Huihai Wang(王会海), and Kehui Sun(孙克辉). Solutions and memory effect of fractional-order chaotic system: A review[J]. 中国物理B, 2022, 31(6): 60501-060501.
[5]	Yue Li(李月), Zengqiang Chen(陈增强), Mingfeng Yuan(袁明峰), and Shijian Cang(仓诗建). The transition from conservative to dissipative flows in class-B laser model with fold-Hopf bifurcation and coexisting attractors[J]. 中国物理B, 2022, 31(6): 60503-060503.
[6]	Peng-Fei Fang(方鹏飞), Han Liu(刘涵), Cheng-Mao Wu(吴成茂), and Min Liu(刘旻). Neural-mechanism-driven image block encryption algorithm incorporating a hyperchaotic system and cloud model[J]. 中国物理B, 2022, 31(4): 40501-040501.
[7]	Li-Ping Zhang(张丽萍), Yang Liu(刘洋), Zhou-Chao Wei(魏周超),Hai-Bo Jiang(姜海波), and Qin-Sheng Bi(毕勤胜). A class of two-dimensional rational maps with self-excited and hidden attractors[J]. 中国物理B, 2022, 31(3): 30503-030503.
[8]	Jun Wang(王君), Yuan-Xi Zhang(张沅熙), Fan Wang(王凡), Ren-Jie Ni(倪仁杰), and Yu-Heng Hu(胡玉衡). Color-image encryption scheme based on channel fusion and spherical diffraction[J]. 中国物理B, 2022, 31(3): 34205-034205.
[9]	Atiyeh Bayani, Sajad Jafari, and Hamed Azarnoush. Explosive synchronization: From synthetic to real-world networks[J]. 中国物理B, 2022, 31(2): 20504-020504.
[10]	Li-Ping Zhang(张丽萍), Yang Liu(刘洋), Zhou-Chao Wei(魏周超), Hai-Bo Jiang(姜海波), Wei-Peng Lyu(吕伟鹏), and Qin-Sheng Bi(毕勤胜). Extremely hidden multi-stability in a class of two-dimensional maps with a cosine memristor[J]. 中国物理B, 2022, 31(10): 100503-100503.
[11]	Fang-Fang Zhang(张芳芳), Rui Gao(高瑞), and Jian Liu(刘坚). Acoustic wireless communication based on parameter modulation and complex Lorenz chaotic systems with complex parameters and parametric attractors[J]. 中国物理B, 2021, 30(8): 80503-080503.
[12]	Tong-Feng Weng(翁同峰), Xin-Xin Cao(曹欣欣), and Hui-Jie Yang(杨会杰). Complex network perspective on modelling chaotic systems via machine learning[J]. 中国物理B, 2021, 30(6): 60506-060506.
[13]	Abdullah Zafar and Majid Khan. Energy behavior of Boris algorithm[J]. 中国物理B, 2021, 30(5): 55203-055203.
[14]	Chenguang Ma(马晨光), Santo Banerjee, Li Xiong(熊丽), Tianming Liu(刘天明), Xintong Han(韩昕彤), and Jun Mou(牟俊). Dynamical analysis, circuit realization, and application in pseudorandom number generators of a fractional-order laser chaotic system[J]. 中国物理B, 2021, 30(12): 120504-120504.
[15]	Quan Xu(徐权), Tong Liu(刘通), Cheng-Tao Feng(冯成涛), Han Bao(包涵), Hua-Gan Wu(武花干), and Bo-Cheng Bao(包伯成). Continuous non-autonomous memristive Rulkov model with extreme multistability[J]. 中国物理B, 2021, 30(12): 128702-128702.