Continuous non-autonomous memristive Rulkov model with extreme multistability

doi:10.1088/1674-1056/ac2f30

中国物理B ›› 2021, Vol. 30 ›› Issue (12): 128702-128702.doi: 10.1088/1674-1056/ac2f30

所属专题： SPECIAL TOPIC — Interdisciplinary physics: Complex network dynamics and emerging technologies

Continuous non-autonomous memristive Rulkov model with extreme multistability

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)^†

School of Microelectronics and Control Engineering, Changzhou University, Changzhou 213164, China

收稿日期:2021-07-15 修回日期:2021-10-09 接受日期:2021-10-13 出版日期:2021-11-15 发布日期:2021-11-30
通讯作者: Bo-Cheng Bao E-mail:mervinbao@126.com
基金资助:
Project supported by the National Natural Science Foundation of China (Grant Nos. 12172066, 61801054, and 51777016), the Natural Science Foundation of Jiangsu Province, China (Grant No. BK20160282), and the Postgraduate Research and Practice Innovation Program of Jiangsu Province, China (Grant No. KYCX21_2823).

Continuous non-autonomous memristive Rulkov model with extreme multistability

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)^†

School of Microelectronics and Control Engineering, Changzhou University, Changzhou 213164, China

Received:2021-07-15 Revised:2021-10-09 Accepted:2021-10-13 Online:2021-11-15 Published:2021-11-30
Contact: Bo-Cheng Bao E-mail:mervinbao@126.com
Supported by:
Project supported by the National Natural Science Foundation of China (Grant Nos. 12172066, 61801054, and 51777016), the Natural Science Foundation of Jiangsu Province, China (Grant No. BK20160282), and the Postgraduate Research and Practice Innovation Program of Jiangsu Province, China (Grant No. KYCX21_2823).

摘要/Abstract

摘要： Based on the two-dimensional (2D) discrete Rulkov model that is used to describe neuron dynamics, this paper presents a continuous non-autonomous memristive Rulkov model. The effects of electromagnetic induction and external stimulus are simultaneously considered herein. The electromagnetic induction flow is imitated by the generated current from a flux-controlled memristor and the external stimulus is injected using a sinusoidal current. Thus, the presented model possesses a line equilibrium set evolving over the time. The equilibrium set and their stability distributions are numerically simulated and qualitatively analyzed. Afterwards, numerical simulations are executed to explore the dynamical behaviors associated to the electromagnetic induction, external stimulus, and initial conditions. Interestingly, the initial conditions dependent extreme multistability is elaborately disclosed in the continuous non-autonomous memristive Rulkov model. Furthermore, an analog circuit of the proposed model is implemented, upon which the hardware experiment is executed to verify the numerically simulated extreme multistability. The extreme multistability is numerically revealed and experimentally confirmed in this paper, which can widen the future engineering employment of the Rulkov model.

关键词: extreme multistability, memristor, electromagnetic induction, Rulkov model

Abstract: Based on the two-dimensional (2D) discrete Rulkov model that is used to describe neuron dynamics, this paper presents a continuous non-autonomous memristive Rulkov model. The effects of electromagnetic induction and external stimulus are simultaneously considered herein. The electromagnetic induction flow is imitated by the generated current from a flux-controlled memristor and the external stimulus is injected using a sinusoidal current. Thus, the presented model possesses a line equilibrium set evolving over the time. The equilibrium set and their stability distributions are numerically simulated and qualitatively analyzed. Afterwards, numerical simulations are executed to explore the dynamical behaviors associated to the electromagnetic induction, external stimulus, and initial conditions. Interestingly, the initial conditions dependent extreme multistability is elaborately disclosed in the continuous non-autonomous memristive Rulkov model. Furthermore, an analog circuit of the proposed model is implemented, upon which the hardware experiment is executed to verify the numerically simulated extreme multistability. The extreme multistability is numerically revealed and experimentally confirmed in this paper, which can widen the future engineering employment of the Rulkov model.

Key words: extreme multistability, memristor, electromagnetic induction, Rulkov model

中图分类号: (Effects of electromagnetic and acoustic fields on biological systems)

87.50.-a

87.19.ll (Models of single neurons and networks) 87.23.Kg (Dynamics of evolution)

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.

参考文献

[1] Yao Z, Zhou P, Zhu Z G and Ma J 2021 Neurocomputing 423 518
[2] Xu L F, Li C D and Chen L 2016 Acta Phys. Sin. 65 240701 (in Chinese)
[3] Hodgkin A L and Huxley A F 1952 J. Physiol. 117 500
[4] Morris C and Lecar H 1981 Biophys. J. 35 193
[5] Chay T R 1985 Physica D 16 233
[6] Xu Q, Tan X, Zhu D, Bao H, Hu Y H and Bao B C 2020 Chaos Solitons Fractals 141 110353
[7] Wilson H R 1999 J. Theor. Biol. 200 375
[8] Hindmarsh J L and Rose R M 1982 Nature 296 162
[9] FitzHugh R 1961 Biophys. J. 1 445
[10] Izhikevich E M 1999 IEEE Trans. Neural Netw. 10 499
[11] Elson R C, Selverston A I, Huerta R, Rulkov N F, Rabinovich M I and Abarbanel H D I 1998 Phys. Rev. Lett. 81 5692
[12] Bao B C, Hu A H, Xu Q, Bao H, Wu H G and Chen M 2018 Nonlinear Dyn. 92 1695
[13] Bao H, Hu A H and Liu W B 2019 Int. J. Bifurc. Chaos 29 1950006
[14] Ge M Y, Jia Y, Xu Y and Yang L J 2018 Nonlinear Dyn. 91 515
[15] Parastesh F, Rajagopal K, Karthikeyan A, Alsaedi A, Hayat T and Pham V T 2018 Cogn. Neurodyn. 12 607
[16] Lv M and Ma J 2016 Neurocomputing 205 375
[17] Qu L H, Du L, Deng Z C, Cao Z L and Hu H W 2018 Chin. Phys. B 27 118707
[18] Yuan Z X, Feng P H, Du M M and Wu Y 2020 Chin. Phys. B 29 030504
[19] Lv M, Wang C N, Ren G D, Ma J and Song X L 2016 Nonlinear Dyn. 85 1479
[20] An X L and Qiao S 2021 Chaos Solitons Fractals 143 110587
[21] Ma J and Tang J 2017 Nonlinear Dyn. 89 1569
[22] Carpenter C J 1999 IEE Proceedings-Science, Measur. Technol. 146 182
[23] Chua L O 2015 Radioengineering 24 319
[24] Xu Q, Lin Y, Bao B C and Chen M 2016 Chaos Solitons Fractals 83 186
[25] Wu F Q, Wang C N, Xu Y and Ma J 2016 Sci. Rep. 6 28
[26] Ma J and Tang J 2017 Nonlinear Dyn. 89 1569
[27] Yu F, Zhang Z N, Shen H, Huang Y Y, Cai S, Jin J and Du S C 2021 Front. Phys. 9 690651
[28] Kafraj M S, Parastesh F and Jafari S 2020 Chaos Solitons Fractals 137 109782
[29] Wang Y, Ma J, Xu Y, Wu F Q and Zhou P 2017 Int. J. Bifurc. Chaos 27 1750030
[30] Jin W Y, Wang A, Ma J and Lin Q 2019 Sci. China Technol. Sci. 62 2113
[31] Ge M Y, Jia Y, Xu Y and Yang L J 2018 Nonlinear Dyn. 91 515
[32] Qu L H, Du L, Hu H W, Cao Z L and Deng Z C 2020 Nonlinear Dyn. 102 2739
[33] Gu H G, Pan B B and Li Y Y 2015 Nonlinear Dyn. 82 1191
[34] Bao H, Hu A H, Liu W B and Bao B C 2020 IEEE Trans. Neural Netw. Learning Sys. 31 502
[35] Lin H R, Wang C H, Sun Y C and Yao W 2020 Nonlinear Dyn. 100 3667
[36] Bao H, Liu W B and Hu A H 2019 Nonlinear Dyn. 95 43
[37] Marco M D, Forti M and Pancioni L 2017 IEEE Trans. Cybernetics 47 2970
[38] Lai Q, Hu B, Guan Z H, Li T, Zheng D F and Wu Y H 2016 Neurocomputing 207 785
[39] Tang Y X, Khalaf A J M, Rajagopal K, Pham V T, Jafari S and Tian Y 2018 Chin. Phys. B 27 040502
[40] Li C B, Xu Y J, Chen G R, Liu Y J and Zheng J C 2019 Nonlinear Dyn. 95 1245
[41] Yu F, Qian S, Chen X, Huang Y Y, Cai S, Jin J and Du S C 2021 Complexity 2021 6683284
[42] Bao H, Liu W B and Chen M 2019 Nonlinear Dyn. 96 1879
[43] Rulkov N F 2002 Phys. Rev. E 65 041922
[44] Wang G H, Peng M S, Zuo J and Cheng R R 2017 Nonlinear Dyn. 89 2553
[45] Li D, Zheng Y and Yang Y 2019 Indian J. Phys. 93 1477
[46] Bashkirtseva I, Nasyrova V and Ryashko L 2020 Int. J. Bifurc. Chaos 30 2050153
[47] Bashkirtseva I, Nasyrova V and Ryashko L 2018 Chaos Soliton Fractals 110 76
[48] Wang C X and Cao H J 2015 Commun. Nonlinear Sci. Numer. Simulat. 20 536
[49] Sun H J and Cao H J 2016 Commun. Nonlinear Sci. Numer. Simulat. 40 15
[50] Budzinski R C, Lopes S R and Masoller C 2021 Neurocomputing 1 44
[51] Sarbendu R, Arnob R, Bera B K and Dibakar G 2018 Nonlinear Dyn. 94 785
[52] Xu Q, Song Z, Bao H, Chen M and Bao B C 2018 AEU-Int. J. Electron. Commun. 96 66
[53] Xu W, Wang Y Q, Li Y F, Gao F, Zhang M C, Lian X J, Wan X, Xiao J and Tong Y 2019 Acta Phys. Sin. 68 238501 (in Chinese)
[54] Chen J C, Chen J Q, Bao H, Chen M and Bao B C 2018 Nonlinear Dyn. 95 3385
[55] Wolf A, Swift J B, Swinney H L and Vastano J A 1985 Physica D 16 285
[56] Bao B C, Xu Q, Bao H and Chen M 2016 Electron. Lett. 52 1008
[57] Bao H, Chen M, Wu H G and Bao B C 2020 Sci. China Tech. Sci. 63 603
[58] Jafari S, Ahmadi A, Khalaf A, Abdolmohammadi H R, Pham V T and Alsaadi F E 2018 Int. J. Electron. Commun. (AEÜ) 89 131
[59] Yuan F, Wang G Y, Shen Y R and Wang X Y 2016 Nonlinear Dyn. 86 37
[60] Bao B C, Zhu Y X, Ma J, Bao H, Wu H G and Chen M 2021 Sci. China Tech. Sci. 64 1107

Continuous non-autonomous memristive Rulkov model with extreme multistability

Continuous non-autonomous memristive Rulkov model with extreme multistability

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]	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.
[2]	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.
[3]	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.
[4]	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.
[5]	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.
[6]	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.
[7]	Ming-Jian Guo(郭明健), Shu-Kai Duan(段书凯), and Li-Dan Wang(王丽丹). Pulse coding off-chip learning algorithm for memristive artificial neural network[J]. 中国物理B, 2022, 31(7): 78702-078702.
[8]	Sheng-Hao Jia(贾生浩), Yu-Xia Li(李玉霞), Qing-Yu Shi(石擎宇), and Xia Huang(黄霞). Design and FPGA implementation of a memristor-based multi-scroll hyperchaotic system[J]. 中国物理B, 2022, 31(7): 70505-070505.
[9]	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). Fabrication and investigation of ferroelectric memristors with various synaptic plasticities[J]. 中国物理B, 2022, 31(7): 78502-078502.
[10]	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). A mathematical analysis: From memristor to fracmemristor[J]. 中国物理B, 2022, 31(6): 60204-060204.
[11]	Yan-Mei Lu(卢艳梅), Chun-Hua Wang(王春华), Quan-Li Deng(邓全利), and Cong Xu(徐聪). The dynamics of a memristor-based Rulkov neuron with fractional-order difference[J]. 中国物理B, 2022, 31(6): 60502-060502.
[12]	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). Memristor-based multi-synaptic spiking neuron circuit for spiking neural network[J]. 中国物理B, 2022, 31(4): 40702-040702.
[13]	Ai-Xue Qi(齐爱学), Bin-Da Zhu(朱斌达), and Guang-Yi Wang(王光义). Complex dynamic behaviors in hyperbolic-type memristor-based cellular neural network[J]. 中国物理B, 2022, 31(2): 20502-020502.
[14]	Qiankun Sun(孙乾坤), Shaobo He(贺少波), Kehui Sun(孙克辉), and Huihai Wang(王会海). A novel hyperchaotic map with sine chaotification and discrete memristor[J]. 中国物理B, 2022, 31(12): 120501-120501.
[15]	Yuan Ge(葛源), Jie Li(李杰), Wenwu Jiang(蒋文武), Lidan Wang(王丽丹), and Shukai Duan(段书凯). A spintronic memristive circuit on the optimized RBF-MLP neural network[J]. 中国物理B, 2022, 31(11): 110702-110702.