A memristive map with coexisting chaos and hyperchaos

doi:10.1088/1674-1056/abf4fb

中国物理B ›› 2021, Vol. 30 ›› Issue (11): 110502-110502.doi: 10.1088/1674-1056/abf4fb

A memristive map with coexisting chaos and hyperchaos

Sixiao Kong(孔思晓)^1,2, Chunbiao Li(李春彪)^1,2,†, Shaobo He(贺少波)³, Serdar Çiçek⁴, and Qiang Lai(赖强)⁵

1 Jiangsu Collaborative Innovation Center of Atmospheric Environment and Equipment Technology(CICAEET), Nanjing University of Information Science & Technology, Nanjing 210044, China;
2 School of Artificial Intelligence, Nanjing University of Information Science & Technology, Nanjing 210044, China;
3 School of Physics and Electronics, Central South University, Changsha 410083, China;
4 Department of Electronic & Automation, Vocational School of Hacıbektaş, Nevşehir Hacı Bektaş Veli University, Hacıbektaş 50800, Nevşehir, Turkey;
5 School of Electrical and Automation Engineering, East China Jiaotong University, Nanchang 330013, China

收稿日期:2021-02-03 修回日期:2021-03-17 接受日期:2021-04-06 出版日期:2021-10-13 发布日期:2021-10-13
通讯作者: Chunbiao Li E-mail:goontry@126.com,chunbiaolee@nuist.edu.cn
基金资助:
Project supported by the National Natural Science Foundation of China (Grant No. 61871230), the Natural Science Foundation of Jiangsu Province, China (Grant No. BK20181410), and the Postgraduate Research and Practice Innovation Project of Jiangsu Province, China (Grant No. SJCX21_0350).

A memristive map with coexisting chaos and hyperchaos

Sixiao Kong(孔思晓)^1,2, Chunbiao Li(李春彪)^1,2,†, Shaobo He(贺少波)³, Serdar Çiçek⁴, and Qiang Lai(赖强)⁵

1 Jiangsu Collaborative Innovation Center of Atmospheric Environment and Equipment Technology(CICAEET), Nanjing University of Information Science & Technology, Nanjing 210044, China;
2 School of Artificial Intelligence, Nanjing University of Information Science & Technology, Nanjing 210044, China;
3 School of Physics and Electronics, Central South University, Changsha 410083, China;
4 Department of Electronic & Automation, Vocational School of Hacıbektaş, Nevşehir Hacı Bektaş Veli University, Hacıbektaş 50800, Nevşehir, Turkey;
5 School of Electrical and Automation Engineering, East China Jiaotong University, Nanchang 330013, China

Received:2021-02-03 Revised:2021-03-17 Accepted:2021-04-06 Online:2021-10-13 Published:2021-10-13
Contact: Chunbiao Li E-mail:goontry@126.com,chunbiaolee@nuist.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Grant No. 61871230), the Natural Science Foundation of Jiangsu Province, China (Grant No. BK20181410), and the Postgraduate Research and Practice Innovation Project of Jiangsu Province, China (Grant No. SJCX21_0350).

摘要/Abstract

摘要： By introducing a discrete memristor and periodic sinusoidal functions, a two-dimensional map with coexisting chaos and hyperchaos is constructed. Various coexisting chaotic and hyperchaotic attractors under different Lyapunov exponents are firstly found in this discrete map, along with which other regimes of coexistence such as coexisting chaos, quasi-periodic oscillation, and discrete periodic points are also captured. The hyperchaotic attractors can be flexibly controlled to be unipolar or bipolar by newly embedded constants meanwhile the amplitude can also be controlled in combination with those coexisting attractors. Based on the nonlinear auto-regressive model with exogenous inputs (NARX) for neural network, the dynamics of the memristive map is well predicted, which provides a potential passage in artificial intelligence-based applications.

关键词: memristor, hyperchaos, coexisting attractors, amplitude control, neural network

Abstract: By introducing a discrete memristor and periodic sinusoidal functions, a two-dimensional map with coexisting chaos and hyperchaos is constructed. Various coexisting chaotic and hyperchaotic attractors under different Lyapunov exponents are firstly found in this discrete map, along with which other regimes of coexistence such as coexisting chaos, quasi-periodic oscillation, and discrete periodic points are also captured. The hyperchaotic attractors can be flexibly controlled to be unipolar or bipolar by newly embedded constants meanwhile the amplitude can also be controlled in combination with those coexisting attractors. Based on the nonlinear auto-regressive model with exogenous inputs (NARX) for neural network, the dynamics of the memristive map is well predicted, which provides a potential passage in artificial intelligence-based applications.

Key words: memristor, hyperchaos, coexisting attractors, amplitude control, neural network

中图分类号: (Nonlinear dynamics and chaos)

05.45.-a

05.45.Ac (Low-dimensional chaos) 05.45.Pq (Numerical simulations of chaotic systems) 05.45.Gg (Control of chaos, applications of chaos)

Sixiao Kong(孔思晓), Chunbiao Li(李春彪), Shaobo He(贺少波), Serdar Çiçek, and Qiang Lai(赖强). A memristive map with coexisting chaos and hyperchaos[J]. 中国物理B, 2021, 30(11): 110502-110502.

Sixiao Kong(孔思晓), Chunbiao Li(李春彪), Shaobo He(贺少波), Serdar Çiçek, and Qiang Lai(赖强). A memristive map with coexisting chaos and hyperchaos[J]. Chin. Phys. B, 2021, 30(11): 110502-110502.

参考文献

[1] Adhikari S P, Sah M, Kim H and Chua L O 2013 IEEE Trans. Circuits I 60 3008
[2] Muthuswamy B and Kokate P P 2009 IETE Tech. Rev. 26 417
[3] Corinto F and Forti M 2017 IEEE Trans. Circuits I 64 1540
[4] Li C B, Thio W J C, Iu H T C and Lu T A 2018 IEEE Access 6 12945
[5] Zhu M H, Wang C H, Deng Q L and Hong Q H 2020 Int. J. Bifur. Chaos 30 2050184
[6] Zhong X, Peng M F and Shahidehpour M 2019 Int. J. Circuit Theory Appl. 47 686
[7] Danca M F, Aziz-Alaoui M A and Small M 2015 Chin. Phys. B 24 060507
[8] Zhang L P, Liu Y, Wei Z C, Jiang H B and Bi Q S 2020 Chin. Phys. B 29 060501
[9] Dudkowski D, Jafari S, Kapitaniak T, Kuznetsov N V, Leonov G A and Prasad A 2016 Phys. Rep. 637 1
[10] Njitacke Z T, Kengne J, Fotsin H B, Negou A N and Tchiotsop D 2016 Chaos Solit. Fract. 91 180
[11] Kengne J, Njitacke Z T and Fotsin H B 2016 Nonlin. Dyn. 83 751
[12] Kong S X, Li C B, Jiang H B, Lai Q and Jiang X W 2021 Chaos 31 043121
[13] Li C B, Sprott J C, Kapitaniak Tomasz and Lu T A 2018 Chaos Solit. Fract. 109 76
[14] Sprott J C, Jafari S, Khalaf A J M and Kapitaniak T 2017 Eur. Phys. J. Special Topics 226 1979
[15] Li C B, Sprott J C and Mei Y 2017 Nonlin. Dyn. 89 2629
[16] Li C B, Sprott J C, Hu W and Xu Y J 2017 Int. J. Bifur. Chaos 27 1750160
[17] Lai Q and Chen S M 2016 Int. J. Bifur. Chaos 26 1650177
[18] Lai Q, Akgul A, Zhao X W and Pei H Q 2017 Int. J. Bifur. Chaos 27 1750142
[19] Li C B, Jiang Y C and Ma X 2021 Chaos Theory Appl. 3 47
[20] Sun J W, Zhao X T, Fang J and Wang Y F 2018 Nonlin. Dyn. 94 2879
[21] Lai Q, Chen C Y, Zhao X W, Kengne J and Volos C 2019 IEEE Access 7 24051
[22] Bao B C, Xu Q, Bao H and Chen M 2016 Electron. Lett. 52 1008
[23] Bao B C, Bao H, Wang N, Chen M and Xu Q 2017 Chaos Solit. Fract. 94 102
[24] Xu Q, Lin Y, Bao B C and Chen M 2016 Chaos Solit. Fract. 83 186
[25] Chen M, Sun M X, Bao B C, Wu H G, Xu Q and Wang J 2018 Nonlin. Dyn. 91 1395
[26] Mezatio B A, Motchongom M T, Tekam B R W, Kengne R, Tchitnga R and Fomethe A 2019 Chaos Solit. Fract. 120 100
[27] Li Z J, Zhou C Y and Wang M J 2019 AEU Int. J. Electron. Commun. 100 127
[28] Chang H, Li Y X, Chen G R and Yuan F 2020 Int. J. Bifur. Chaos 30 2030019
[29] Peng Y X, Sun K H and He S B 2020 Chaos Solit. Fract. 137 109873
[30] Bao B C, Li H Z, Wu H G, Zhang X and Chen M 2020 Electron. Lett. 56 769
[31] He S B, Sun K H, Peng Y X and Wang L 2020 AIP Adv. 100 15332
[32] Peng Y X, He S B and Sun K H 2021 AEU Int. J. Electron. C 129 153539
[33] He S B 2020 Front. Appl. Math. Statist. 6 24
[34] Bilal A, Erhan A and Bedri O 2009 Chaos Solit. Fract. 40 1715
[35] Gaganpreet K and Sankalap A 2018 J. Comput. Des. Eng. 5 275
[36] Yang L J and Chen T J 2002 Commun. Theor. Phys. 38 168
[37] Karunasinghe D S K and Liong S Y 2006 J. Hydrol. 323 92
[38] Woolley J W, Agarwal P K and Baker J 2010 Int. J. Numer. Methods Fluids 63 989
[39] Rafsanjani M K and Samareh M 2016 J. Comput. Methods Sci. Eng. 16 599
[40] Raissi M, Perdikaris P and karniadakis G E 2018 arXiv:1811.05537 [math.NA]
[41] Qin T, Wu K L and Xiu D B 2019 J. Comput. Phys. 395 620
[42] Zang C X and Wang F 2019 Proceedings of the 26th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, August 4-8, 2019, Anchorage, AK, USA, pp. 892-902
[43] Bevi A R, Tumu S and Prasad N V 2018 Comput. Electr. Eng. 72 179
[44] Alcin M, Koyuncu I, Tuna M, Varan M and Pehlivan I 2019 Int. J. Circuit Theory Appl. 47 365
[45] Ni J K, Liu C X, Liu K and Liu L 2014 Chin. Phys. B 23 100504
[46] Zhang Z Y, Feng X Q, Yao Z H and Jia H Y 2015 Chin. Phys. B 24 110503
[47] Liu H, Li S G, Sun Y G and Wang H X 2015 Chin. Phys. B 24 090505
[48] Li C B, Wang X and Chen G R 2017 Nonlin. Dyn. 90 1335
[49] Taqvi S A, Tufa L D, Zabiri H, Maulud A S and Uddin F 2020 Neural Comput. Appl. 32 3503
[50] Chen C, Sun K H and He S B 2019 Signal Process. 168 107340
[51] Wang X Y, Wang Y, Wang S W, Zhang Y Q and Wu X J 2018 Chin. Phys. B 27 110502
[52] Deng J, Zhou M J and Wang C H, Wang S C and Xu C 2021 Multimed. Tools Appl. 80 13821
[53] Zeng J and Wang C H 2021 Secur. Commun. Netw. 5 1

A memristive map with coexisting chaos and hyperchaos

A memristive map with coexisting chaos and hyperchaos

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]	Keyi Peng(彭珂依), Jing Yue(岳靖), Wen Zhang(张文), and Jian Li(李剑). Meshfree-based physics-informed neural networks for the unsteady Oseen equations[J]. 中国物理B, 2023, 32(4): 40208-040208.
[2]	Hai-Chao Zhan(詹海潮), Bing Chen(陈兵), Yi-Xiang Peng(彭怡翔), Le Wang(王乐), Wen-Nai Wang(王文鼐), and Sheng-Mei Zhao(赵生妹). Diffraction deep neural network based orbital angular momentum mode recognition scheme in oceanic turbulence[J]. 中国物理B, 2023, 32(4): 44208-044208.
[3]	Ting Zhou(周婷), Xing Gao(高星), Zhiwei Ma(马志伟), Hailong Chang(常海龙), Tielong Shen(申铁龙), Minghuan Cui(崔明焕), and Zhiguang Wang(王志光). Atomistic insights into early stage corrosion of bcc Fe surfaces in oxygen dissolved liquid lead-bismuth eutectic (LBE-O)[J]. 中国物理B, 2023, 32(3): 36801-036801.
[4]	Yong-Tao Yu(于永涛) and Xiao-Li Yang(杨晓丽). Inverse stochastic resonance in modular neural network with synaptic plasticity[J]. 中国物理B, 2023, 32(3): 30201-030201.
[5]	Zhan-Hong Guo(郭展宏), Zhi-Jun Li(李志军), Meng-Jiao Wang(王梦蛟), and Ming-Lin Ma(马铭磷). Hopf bifurcation and phase synchronization in memristor-coupled Hindmarsh-Rose and FitzHugh-Nagumo neurons with two time delays[J]. 中国物理B, 2023, 32(3): 38701-038701.
[6]	Ying Wang(王莹), Feng Qi(祁峰), Zi-Xu Zhang(张子旭), and Jin-Kuan Wang(汪晋宽). Super-resolution reconstruction algorithm for terahertz imaging below diffraction limit[J]. 中国物理B, 2023, 32(3): 38702-038702.
[7]	Fan Sun(孙帆), Jing Su(粟静), Jie Li(李杰), Shukai Duan(段书凯), and Xiaofang Hu(胡小方). Memristor's characteristics: From non-ideal to ideal[J]. 中国物理B, 2023, 32(2): 28401-028401.
[8]	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.
[9]	Xi Zhu(朱熙), Hui Xu(徐晖), Weiping Yang(杨为平), Zhiwei Li(李智炜), Haijun Liu(刘海军), Sen Liu(刘森), Yinan Wang(王义楠), and Hongchang Long(龙泓昌). High throughput N-modular redundancy for error correction design of memristive stateful logic[J]. 中国物理B, 2023, 32(1): 18502-018502.
[10]	Xiao-Juan Lian(连晓娟), Jin-Ke Fu(付金科), Zhi-Xuan Gao(高志瑄),Shi-Pu Gu(顾世浦), and Lei Wang(王磊). High-performance artificial neurons based on Ag/MXene/GST/Pt threshold switching memristors[J]. 中国物理B, 2023, 32(1): 17304-017304.
[11]	Zhi-Jun Li(李志军), Wen-Qiang Xie(谢文强), Jin-Fang Zeng(曾金芳), and Yi-Cheng Zeng(曾以成). Firing activities in a fractional-order Hindmarsh-Rose neuron with multistable memristor as autapse[J]. 中国物理B, 2023, 32(1): 10503-010503.
[12]	Jian Zhang(张健), Yiming Liu(刘一鸣), and Zhanchun Tu(涂展春). Exploring fundamental laws of classical mechanics via predicting the orbits of planets based on neural networks[J]. 中国物理B, 2022, 31(9): 94502-094502.
[13]	Jin Xu(徐瑾), Xiaoguang Chen(陈晓光), Rong Zhang(张蓉), and Hanwei Xiao(肖晗微). Purification in entanglement distribution with deep quantum neural network[J]. 中国物理B, 2022, 31(8): 80304-080304.
[14]	Tong-Bao Zhang(张同宝), Hui-Jian Liang(梁慧剑),Shi-Guang Wang(王时光), and Chen-Guang Ouyang(欧阳晨光). Ionospheric vertical total electron content prediction model in low-latitude regions based on long short-term memory neural network[J]. 中国物理B, 2022, 31(8): 80701-080701.
[15]	Weijin Li(李伟进), Yuhao Ren(任昱昊), and Fabing Duan(段法兵). Hyperparameter on-line learning of stochastic resonance based threshold networks[J]. 中国物理B, 2022, 31(8): 80503-080503.