Please wait a minute...
Chin. Phys. B, 2024, Vol. 33(5): 050504    DOI: 10.1088/1674-1056/ad1dcc
GENERAL Prev   Next  

Dynamics and synchronization of neural models with memristive membranes under energy coupling

Jingyue Wan(万婧玥)1, Fuqiang Wu(吴富强)1,2,†, Jun Ma(马军)3, and Wenshuai Wang(汪文帅)1,2
1 School of Mathematics and Statistics, Ningxia University, Yinchuan 750021, China;
2 Ningxia Basic Science Research Center of Mathematics, Ningxia University, Yinchuan 750021, China;
3 Department of Physics, Lanzhou University of Technology, Lanzhou 730050, China
Abstract  Dynamical modeling of neural systems plays an important role in explaining and predicting some features of biophysical mechanisms. The electrophysiological environment inside and outside of the nerve cell is different. Due to the continuous and periodical properties of electromagnetic fields in the cell during its operation, electronic components involving two capacitors and a memristor are effective in mimicking these physical features. In this paper, a neural circuit is reconstructed by two capacitors connected by a memristor with periodical mem-conductance. It is found that the memristive neural circuit can present abundant firing patterns without stimulus. The Hamilton energy function is deduced using the Helmholtz theorem. Further, a neuronal network consisting of memristive neurons is proposed by introducing energy coupling. The controllability and flexibility of parameters give the model the ability to describe the dynamics and synchronization behavior of the system.
Keywords:  memristor      neuronal model      energy      synchronization  
Received:  06 December 2023      Revised:  29 December 2023      Accepted manuscript online:  12 January 2024
PACS:  05.45.Pq (Numerical simulations of chaotic systems)  
  05.45.Xt (Synchronization; coupled oscillators)  
  05.45.Gg (Control of chaos, applications of chaos)  
Fund: This study was funded by the National Natural Science Foundation of China (Grant No. 12302070) and the Ningxia Science and Technology Leading Talent Training Program (Grant No. 2022GKLRLX04).
Corresponding Authors:  Fuqiang Wu     E-mail:  alexwutian@nxu.edu.cn

Cite this article: 

Jingyue Wan(万婧玥), Fuqiang Wu(吴富强), Jun Ma(马军), and Wenshuai Wang(汪文帅) Dynamics and synchronization of neural models with memristive membranes under energy coupling 2024 Chin. Phys. B 33 050504

[1] Friston K 2010 Nat. Rev. Neurosci. 11 127
[2] Moujahid A, D’Anjou A, Torrealdea F J and Torrealdea F 2011 Phys. Rev. E 83 031912
[3] Li S and Sheng Z H 2022 Nat. Rev. Neurosci. 23 4
[4] Nowotny T and Rabinovich M I 2007 Phys. Rev. Lett. 98 128106
[5] Canavier C C, Clark J W and Byrne J H 1990 Biophys. J. 57 1245
[6] Rabinovich M I, Varona P, Selverston A I and Abarbanel H D I 2006 Rev. Mod. Phys. 78 1213
[7] Hodgkin A L and Huxley A F 1952 J. Physiol. 117 500
[8] Chua L, Sbitnev V and Kim H 2012 Int. J. Bifurcat. Chaos 22 1230011
[9] Sah M P, Kim H and Chua L O 2014 IEEE Circ. Syst. Mag. 14 12
[10] Lv M, Wang C N, Ren G D, Ma J and Song X L 2016 Nonlinear Dyn. 85 1479
[11] Lv M and Ma J 2016 Neurocomputing 205 375
[12] Bao H, Hu A H, Liu W B and Bao B C 2020 IEEE T. Neur. Net. Lear. 31 502
[13] Ding S, Wang N, Bao H, Chen B, Wu H and Xu Q 2023 Chaos Soliton. Fract. 166 112899
[14] Xie Y, Yao Z, Hu X K and Ma J 2021 Chin. Phys. B 30 120510
[15] Zhang X F and Ma J 2021 Journal of Zhejiang University: Science A 22 707
[16] Shen H, Yu F, Wang C H, Sun J R and Cai S 2022 Nonlinear Dyn. 110 3807
[17] Wu F Q and Yao Z 2023 Nonlinear Dyn. 111 13481
[18] Wu F Q, Guo Y T, Ma J and Jin W Y 2023 Appl. Math. Comput. 455 128131
[19] Wu F Q, Guo Y T and Ma J 2022 Nonlinear Dyn. 109 2063
[20] Zhang Y, Xu Y, Yao Z and Ma J 2020 Nonlinear Dyn. 102 1849
[21] Wu F Q, Hu X K and Ma J 2022 Appl. Math. Comput. 432 127366
[22] Guo Y, Wu F, Yang F and Ma J 2023 Chaos 33 113106
[23] Xu Q, Ju Z, Ding S, Feng C, Chen M and Bao B C 2022 Cogn. Neurodyn. 16 1221
[24] Zhang H, Wang L, Zhang P, Zhang X F and Ma J 2021 Chin. Phys. B 30 038702
[25] Qiao S, Gao C H and An X L 2023 Nonlinear Dyn. 111 10529
[26] An X L, Xiong L, Shi Q, Qiao S and Zhang L 2023 Nonlinear Dyn. 111 9509
[27] Ma J and Tang J 2015 Sci. China Technol. Sc. 58 2038
[28] Yang F F, Wang Y and Ma J 2023 Commun. Nonlinear Sci. 119 107127
[29] Xie Y, Yao Z and Ma J 2022 Front. Inform. Technol. Electron. Eng. 23 1407
[30] Ma J 2024 Appl. Math. Comput. 463 128379
[31] Xie Y, Zhou P and Ma J 2023 Appl. Math. Model. 113 175
[32] Xie Y, Zhou P, Yao Z and Ma J 2022 Physica A 607 128175
[33] Torrealdea F J, D’Anjou A, Graña M and Sarasola C 2006 Phys. Rev. E 74 011905
[34] Liu Z L, Yu Y and Wang Q Y 2022 Sci. China Technol. Sc. 65 1435
[35] Liu Z, Han F and Wang Q Y 2022 Nonlinear Dyn. 108 1849
[36] Torrealdea F J, Sarasola C and d’Anjou A 2009 Chaos Soliton. Fract. 40 60
[37] Wu F Q and Wang R B 2023 Commun. Nonlinear Sci. 126 107459
[38] Zhou P, Zhang X F and Ma J 2022 Nonlinear Dyn. 108 1681
[39] Wu F Q, Ma J and Zhang G 2020 Sci. China Technol. Sc. 63 625
[40] Xie Y, Xu Y and Ma J 2023 Nonlinear Dyn. 111 11521
[41] Xie Y and Ma J 2022 J. Biol. Phys. 48 339
[42] Xie Y, Yao Z and Ma J 2023 Sci. China Technol. Sc. 66 439
[43] Yang Z, Zhang Y and Wu F Q 2020 Nonlinear Dyn. 100 647
[44] Usha K and Subha P A 2019 Chin. Phys. B 28 020502
[45] Malik S A and Mir A H 2020 Neural Networks 123 372
[46] Herz A V M, Gollisch T, Machens C K and Jaeger D 2006 Science 314 80
[47] Wu F Q, Meng H and Ma J 2024 Neural Networks 169 607
[48] Barry J F, Turner M J, Schloss J M, Glenn D R, Song Y, Lukin M D, Park H and Walsworth R L 2016 Proc. Natl. Acad. Sci. USA 113 14133
[49] Chua L O 1971 IEEE T. Circ. Theory 18 507
[50] Song X L, Jin W Y and Ma J 2015 Chin. Phys. B 24 128710
[51] Sarasola C, Torrealdea F J, D’Anjou A, Moujahid A and Graña M 2004 Phys. Rev. E 69 011606
[52] Heitmann S, Aburn M J and Breakspear M 2018 Neurocomputing 315 82
[1] Reanalysis of energy band structure in the type-II quantum wells
Xinxin Li(李欣欣), Zhen Deng(邓震), Yang Jiang(江洋), Chunhua Du(杜春花), Haiqiang Jia(贾海强), Wenxin Wang(王文新), and Hong Chen(陈弘). Chin. Phys. B, 2024, 33(6): 067302.
[2] Synchronization and firing mode transition of two neurons in a bilateral auditory system driven by a high-low frequency signal
Charles Omotomide Apata, Yi-Rui Tang(唐浥瑞), Yi-Fan Zhou(周祎凡), Long Jiang(蒋龙), and Qi-Ming Pei(裴启明). Chin. Phys. B, 2024, 33(5): 058704.
[3] Cooperative activation of sodium channels for downgrading the energy efficiency in neuronal information processing
Haoran Yan(严浩然), Jiaqi Yan(颜家琦), Lianchun Yu(俞连春), and Yu-Feng Shao(邵玉峰). Chin. Phys. B, 2024, 33(5): 058801.
[4] Fractional-order heterogeneous memristive Rulkov neuronal network and its medical image watermarking application
Dawei Ding(丁大为), Yan Niu(牛炎), Hongwei Zhang(张红伟), Zongli Yang(杨宗立), Jin Wang(王金), Wei Wang(王威), and Mouyuan Wang(王谋媛). Chin. Phys. B, 2024, 33(5): 050503.
[5] Atomistic understanding of capacity loss in LiNiO2 for high-nickel Li-ion batteries: First-principles study
Shuai Peng(彭率), Li-Juan Chen(陈丽娟), Chang-Chun He(何长春), and Xiao-Bao Yang(杨小宝). Chin. Phys. B, 2024, 33(5): 058201.
[6] Dynamic analysis of a novel multilink-spring mechanism for vibration isolation and energy harvesting
Jia-Heng Xie(谢佳衡), Tao Yang(杨涛), and Jie Tang(唐介). Chin. Phys. B, 2024, 33(5): 050706.
[7] Chimera states of phase oscillator populations with nonlocal higher-order couplings
Yonggang Wu(伍勇刚), Huajian Yu(余华健), Zhigang Zheng(郑志刚), and Can Xu(徐灿). Chin. Phys. B, 2024, 33(4): 040504.
[8] Dynamical behaviors in discrete memristor-coupled small-world neuronal networks
Jieyu Lu(鲁婕妤), Xiaohua Xie(谢小华), Yaping Lu(卢亚平), Yalian Wu(吴亚联), Chunlai Li(李春来), and Minglin Ma(马铭磷). Chin. Phys. B, 2024, 33(4): 048701.
[9] Dynamics analysis and cryptographic implementation of a fractional-order memristive cellular neural network model
Xinwei Zhou(周新卫), Donghua Jiang(蒋东华), Jean De Dieu Nkapkop, Musheer Ahmad, Jules Tagne Fossi, Nestor Tsafack, and Jianhua Wu(吴建华). Chin. Phys. B, 2024, 33(4): 040506.
[10] Coexistence behavior of asymmetric attractors in hyperbolic-type memristive Hopfield neural network and its application in image encryption
Xiaoxia Li(李晓霞), Qianqian He(何倩倩), Tianyi Yu(余天意),Zhuang Cai(才壮), and Guizhi Xu(徐桂芝). Chin. Phys. B, 2024, 33(3): 030505.
[11] Effects of connected automated vehicle on stability and energy consumption of heterogeneous traffic flow system
Jin Shen(申瑾), Jian-Dong Zhao(赵建东), Hua-Qing Liu(刘华清), Rui Jiang(姜锐), and Zhi-Xin Yu(余智鑫). Chin. Phys. B, 2024, 33(3): 030504.
[12] Parametric instability in the pure-quartic nonlinear Schrödinger equation
Yun-Hong Zhang(张云红) and Chong Liu(刘冲). Chin. Phys. B, 2024, 33(3): 030506.
[13] Symmetric Brownian motor subjected to Lévy noise
Kao Jia(贾考), Lan Hu(胡兰), and Linru Nie(聂林如). Chin. Phys. B, 2024, 33(2): 020502.
[14] Electronic property and topological phase transition in a graphene/CoBr2 heterostructure
Yuan-Xiu Qin(秦元秀), Sheng-Shi Li(李胜世), Wei-Xiao Ji(纪维霄), and Chang-Wen Zhang(张昌文). Chin. Phys. B, 2024, 33(2): 027901.
[15] Dynamical behavior of memristor-coupled heterogeneous discrete neural networks with synaptic crosstalk
Minglin Ma(马铭磷), Kangling Xiong(熊康灵), Zhijun Li(李志军), and Shaobo He(贺少波). Chin. Phys. B, 2024, 33(2): 028706.
No Suggested Reading articles found!