Please wait a minute...
Chin. Phys. B, 2021, Vol. 30(11): 110502    DOI: 10.1088/1674-1056/abf4fb
GENERAL Prev   Next  

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
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.
Keywords:  memristor      hyperchaos      coexisting attractors      amplitude control      neural network  
Received:  03 February 2021      Revised:  17 March 2021      Accepted manuscript online:  06 April 2021
PACS:  05.45.-a (Nonlinear dynamics and chaos)  
  05.45.Ac (Low-dimensional chaos)  
  05.45.Pq (Numerical simulations of chaotic systems)  
  05.45.Gg (Control of chaos, applications of chaos)  
Fund: 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).
Corresponding Authors:  Chunbiao Li     E-mail:  goontry@126.com,chunbiaolee@nuist.edu.cn

Cite this article: 

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 2021 Chin. Phys. B 30 110502

[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
[1] Exploring fundamental laws of classical mechanics via predicting the orbits of planets based on neural networks
Jian Zhang(张健), Yiming Liu(刘一鸣), and Zhanchun Tu(涂展春). Chin. Phys. B, 2022, 31(9): 094502.
[2] Purification in entanglement distribution with deep quantum neural network
Jin Xu(徐瑾), Xiaoguang Chen(陈晓光), Rong Zhang(张蓉), and Hanwei Xiao(肖晗微). Chin. Phys. B, 2022, 31(8): 080304.
[3] Ionospheric vertical total electron content prediction model in low-latitude regions based on long short-term memory neural network
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). Chin. Phys. B, 2022, 31(8): 080701.
[4] Hyperparameter on-line learning of stochastic resonance based threshold networks
Weijin Li(李伟进), Yuhao Ren(任昱昊), and Fabing Duan(段法兵). Chin. Phys. B, 2022, 31(8): 080503.
[5] Fabrication and investigation of ferroelectric memristors with various synaptic plasticities
Qi Qin(秦琦), Miaocheng Zhang(张缪城), Suhao Yao(姚苏昊), Xingyu Chen(陈星宇), Aoze Han(韩翱泽),Ziyang Chen(陈子洋), Chenxi Ma(马晨曦), Min Wang(王敏), Xintong Chen(陈昕彤), Yu Wang(王宇),Qiangqiang Zhang(张强强), Xiaoyan Liu(刘晓燕), Ertao Hu(胡二涛), Lei Wang(王磊), and Yi Tong(童祎). Chin. Phys. B, 2022, 31(7): 078502.
[6] Design and FPGA implementation of a memristor-based multi-scroll hyperchaotic system
Sheng-Hao Jia(贾生浩), Yu-Xia Li(李玉霞), Qing-Yu Shi(石擎宇), and Xia Huang(黄霞). Chin. Phys. B, 2022, 31(7): 070505.
[7] Pulse coding off-chip learning algorithm for memristive artificial neural network
Ming-Jian Guo(郭明健), Shu-Kai Duan(段书凯), and Li-Dan Wang(王丽丹). Chin. Phys. B, 2022, 31(7): 078702.
[8] Digraph states and their neural network representations
Ying Yang(杨莹) and Huaixin Cao(曹怀信). Chin. Phys. B, 2022, 31(6): 060303.
[9] A mathematical analysis: From memristor to fracmemristor
Wu-Yang Zhu(朱伍洋), Yi-Fei Pu(蒲亦非), Bo Liu(刘博), Bo Yu(余波), and Ji-Liu Zhou(周激流). Chin. Phys. B, 2022, 31(6): 060204.
[10] The dynamics of a memristor-based Rulkov neuron with fractional-order difference
Yan-Mei Lu(卢艳梅), Chun-Hua Wang(王春华), Quan-Li Deng(邓全利), and Cong Xu(徐聪). Chin. Phys. B, 2022, 31(6): 060502.
[11] Fast prediction of aerodynamic noise induced by the flow around a cylinder based on deep neural network
Hai-Yang Meng(孟海洋), Zi-Xiang Xu(徐自翔), Jing Yang(杨京), Bin Liang(梁彬), and Jian-Chun Cheng(程建春). Chin. Phys. B, 2022, 31(6): 064305.
[12] Memristor-based multi-synaptic spiking neuron circuit for spiking neural network
Wenwu Jiang(蒋文武), Jie Li(李杰), Hongbo Liu(刘洪波), Xicong Qian(钱曦聪), Yuan Ge(葛源), Lidan Wang(王丽丹), and Shukai Duan(段书凯). Chin. Phys. B, 2022, 31(4): 040702.
[13] High-fidelity resonant tunneling passage in three-waveguide system
Rui-Qiong Ma(马瑞琼), Jian Shi(时坚), Lin Liu(刘琳), Meng Liang(梁猛), Zuo-Liang Duan(段作梁), Wei Gao(高伟), and Jun Dong(董军). Chin. Phys. B, 2022, 31(2): 024202.
[14] Parameter estimation of continuous variable quantum key distribution system via artificial neural networks
Hao Luo(罗浩), Yi-Jun Wang(王一军), Wei Ye(叶炜), Hai Zhong(钟海), Yi-Yu Mao(毛宜钰), and Ying Guo(郭迎). Chin. Phys. B, 2022, 31(2): 020306.
[15] Complex dynamic behaviors in hyperbolic-type memristor-based cellular neural network
Ai-Xue Qi(齐爱学), Bin-Da Zhu(朱斌达), and Guang-Yi Wang(王光义). Chin. Phys. B, 2022, 31(2): 020502.
No Suggested Reading articles found!