期刊信息

  • 刊名： 河北师范大学学报（自然科学版）Journal of Hebei Normal University (Natural Science)
  • 主办： 河北师范大学
  • ISSN： 1000-5854
  • CN： 13-1061/N
  • 中国科技核心期刊
  • 中国期刊方阵入选期刊
  • 中国高校优秀科技期刊
  • 华北优秀期刊
  • 河北省优秀科技期刊

协同采编系统

友情链接

电场作用下改进HR神经元模型的动力学行为

  • (1.兰州文理学院 教育学院,甘肃 兰州 730010； 2.兰州交通大学 数理学院,甘肃 兰州 730070)
  • DOI： 10.13763/j.cnki.jhebnu.nse.202302022

Dynamical Behavior of an Improved HR Neuron Model Under Electric Field

摘要/Abstract

摘要：

生物神经细胞内钾、钠和钙离子的跨膜运动将伴随着时变的电磁场，其中激发的电场能够实现对生物神经活动的进一步调制.主要运用非线性理论和数值模拟方案，建立并揭示了一类四维Hindmarsh-Rose(HR)神经元模型的时变稳定性以及全局动力学行为.基于理论分析证实了该非自治的模型存在3种类型的平衡点以及时变稳定性，这也为多吸引子共存提供了理论的依据.此外，得益于双参数分岔图，揭示了该模型的自组织特征，包括“梳”状的混沌结构、倍周期分岔甚至加周期分岔模式.与此同时，神经系统不可避免地受到时变的外界电场扰动，从而导致该模型产生更加复杂的放电活动，并借助于吸引域阐明了丰富的多吸引子共存行为，研究结论可以为进一步探讨外电场效应下神经元复杂的动力学特性提供参考.

Abstract：

The movement of large amounts of ions，sush as potassium,sodium,and calcium ions,in the nervous system triggers time-varying electromagnetic fields that further regulate the firing activity of neurons.The discharge characteristics of an improved Hindmarsh-Rose (HR) neuron model under electric field are studied by numerical simulation.Based on the theoretical analysis,it is proved that the non-autonomous model has three kinds of equilibrium points and time-varying stability,which also provides a theoretical basis for the coexistence of multiple attractors.In addition,by two-parametric bifurcation analysis,we also find that the model generally has a comb-shaped chaotic structure and a chaotic (or non-chaotic) period-adding bifurcation mode.Considering that the electric field is inevitably disturbed periodically,the discharge mode of this model is more complex and has abundant co-existing oscillation modes.The results will provide a useful reference for further studying on the complex dynamic characteristics of neurons under electric field.

关键词

关键词： 神经元模型； 放电活动； 双参数分岔； 共存吸引子； 加周期分岔
Key words： neuron model ; firing activity ; two-parameters bifurcation ; coexisting attractors ; period-adding bifurcation

参考文献 30

  • [1] GU H G,PAN B B.A Fourdimensional Neuronal Model to Describe the Complex Nonlinear Dynamics Observed in the Firing Patterns of a Sciatic Nerve Chronic Constriction Injury Model[J].Nonlinear Dynamics,2015,81:2107-2126.doi:10.1007/s11071-015-2129-7
  • [2] JIA B.Experimental Identification of a Comb-shaped Chaotic Region in Multiple Parameter Spaces Simulated by the HindmarshRose Neuron Model[J].Chinese Physics B,2014(3):179-185.doi:10.1088/1674-1056/23/3/030505
  • [3] AN X L,QIAO S.The Hidden,Period-adding,Mixed-mode Oscillations and Control in a HR Neuron Under Electromagnetic Induction[J].Chaos,Solitons and Fractals,2021,143:110587.doi:10.1016/j.chaos.2020.110587
  • [4] WANG C N,LIU Z L,HOBINY A,et al.Capturing and Shunting Energy in Chaotic Chua Circuit[J].Chaos Solitons & Fractals,2020,134:109697.doi:10.1016/j.chaos.2020.109697
  • [5] XU Y,GUO Y Y,REN G D,et al.Dynamics and Stochastic Resonance in a Thermosensitive Neuron[J].Applied Mathematics and Computation,2020,385:125427.doi:10.1016/j.amc.2020.125427
  • [6] YANG M B,AN S C,GU H G,et al.Understanding of Physiological Neural Firing Patterns Through Dynamical Bifurcation Machineries[J].Neuron Report,2006,17(10):995-999.doi:10.1097/01.wnr.0000224770.74528.d6
  • [7] PARK S,CHU M,KIM J,et al.Electronic System with Memristive Synapses for Pattern Recognition[J].Scientific Reports,2015,5(3):10123.doi:10.1038/srep10123
  • [8] HODGKIN A L,HUXLEY A F.The Components of Membrane Conductance in the Giant Axon of Loligo[J].The Journal of Physiology,1952,116(4):473496.doi:10.1113/jphysiol.1952.sp004718
  • [9] MORRIS C,LECAR H.Voltage Oscillations in the Barnacle Giant Muscle Fiber[J].Biophysical Journal,1981,35(1):193-213.doi:10.1016/s0006-3495(81)84782-0
  • [10] HINDMARSH J L,ROSE R M.A Model of the Nerve Impulse Using Two First-order Differential Equations[J].Nature,1982,296(5853):162-164.doi:10.1038/296162a0
  • [11] WILSON H R.Simplified Dynamics of Human and Mammalian Neocortical Neurons[J].Journal of Theoretical Biology,1999,200(4):375-388.doi:10.1006/jtbi.1999.1002
  • [12] WANG Q Y,LU Q S,CHEN G R,et al.Chaos Synchronization of Coupled Neurons with Gap Junctions[J].Physics Letters A,2011,356(3):17-25.doi:10.1016/j.physleta.2006.03.017
  • [13] WU K J,WANG T J,WANG C N,et al.Study on Electrical Synapse Coupling Synchronization of Hindmarsh-Rose Neurons Under Gaussian White Noise[J].Neural Computing & Applications,2016(3):1-11.doi:10.1007/s00521-016-2681-1
  • [14] 邬开俊,王春丽,单亚州,等.噪声作用下的化学突触耦合神经元系统的同步[J].吉林大学学报(工学版),2017,47(5):1554-1560.doi:10.13229/j.cnki.jdxbgxb201705030 WU Kaijun,WANG Chunli,SHAN Yazhou,et al.Chemical Synapse Coupling Synchronization of HindmarshRose Neurons Under Gauss White Noise[J].Journal of Jilin University(Engineering and Technology),2017,47(5):1554-1560.
  • [15] ANDRIEVSKY B.Adaptive Synchronization Methods for Signal Transmission on Chaotic Carriers[J].Mathematics and Computers in Simulation,2012,58(4/6):285-293.doi:10.1016/s03784754(01)00373-1
  • [16] XUE H W,DU J,LI S L,et al.Region of Interest Encryption for Color Images Based on a Hyperchaotic System with Three Positive Lyapunovexponents[J].Optics & Laser Technology,2018,106:506-516.doi:10.1016/j.optlastec.2018.04.030
  • [17] YANG Z L,LIANG T,DING D W,et al.Dynamic Behavior of Fractional-order Memristive Time-delay System and Image Encryption Application[J].Modern Physics Letters B,2021，35(16):2150271.doi:10.1142/s0217984921502717
  • [18] RECH P C.Dynamics in the Parameter Space of a Neuron Model[J].Chinese Physics Letters,2012,29(6):60506-60509.doi:10.1088/0256-307X/29/6/060506
  • [19] MA J,TANG J.A Review for Dynamics of Collective Behaviors of Network of Neurons[J].Science China Technological Sciences,2015,58(12):2038-2045.doi:10.1007/s11431-015-5961-6
  • [20] LV M,WANG C N,REN G D,et al.Model of Electrical Activity in a Neuron Under Magnetic Flow Effect[J].Nonlinear Dynamics,2016,85(3):1479-1490.doi:10.1007/s11071-016-2773-6
  • [21] 吕密.电磁辐射下神经元的建模及其动力学分析[D].兰州：兰州理工大学,2017.doi:2.1017.860667 LYU Mi.Model Setting and Dynamic Analysis of a Neuron Under Electromagnetic Radiation[D].Lanzhou:Lanzhou University of Technology,2017.
  • [22] 乔帅,安新磊,王红梅,等.电磁感应下HR神经元模型的分岔分析与控制[J].山东大学学报(理学版),2020,55(9):1-9.doi:10.6040/j.issn.1671-9352.0.2019.634 QIAO Shuai,AN Xinlei,WANG Hongmei,et al.Bifurcation Analysis and Control of HR Neuron Model Under Electromagnetic Induction[J].Journal of Shandong University(Natural Science),2020,55(9):1-9.
  • [23] 乔帅,安新磊,王红梅,等.磁通e-HR神经元隐藏放电与分岔行为的研究[J].云南大学学报(自然科学版),2020,42(4):485-494.doi:10.7540/j.ynu.20190642 QIAO Shuai,AN Xinlei,WANG Hongmei,et al.Hidden Discharge and Bifurcation Behavior of Magnetic Fluxe-HR Neurons[J].Journal of Yunnan University(Natural Science),2020,42(4):485-494.
  • [24] MA J,ZHANG G,HAYAT T,et al.Model Electrical Activity of Neuron Under Electric Field[J].Nonlinear Dynamics,2019,95:1585-1598.doi:10.1007/s11071-018-4646-7
  • [25] YAN B,PANAHI S,HE S,et al.Further Dynamical Analysis of Modified Fitzhugh-Nagumo Model Under the Electric Field[J].Nonlinear Dynamics,2020,101:521-529.doi:10.1007/s11071-020-05816-y
  • [26] QIAO S,AN X L.Dynamic Expression of HR Neuron Model Under Electric Field[J].International Journal of Modern Physics B,2021,35(2):2150024.doi:10.1142/s0217979221500247
  • [27] 祁慧敏,张莉,安新磊,等.电场下HR神经元的分岔分析及其同步[J].河北师范大学学报(自然科学版),2021,45(1):39-45.doi:10.13763/j.cnki.jhebnu.nse.202102003 QI Huimin,ZHANG Li,AN Xinlei,et al.Bifurcation Analysis and Synchronization of HR Neurons Under Electric Field[J].Journal of Hebei Normal University(Natural Science),2021,45(1):39-45.
  • [28] WOUAPI K M,FOTSIN B H,LOUODOP F P,et al.Various Firing Activities and Finite-time Synchronization of an Improved Hindmarsh Rose Neuron Model Under Electric Field Effect[J].Cognitive Neuron Dynamics,2020,14(3):375-397.doi:10.1007/s11571-020-09570-0
  • [29] 彭建奎.电磁感应下神经元模型的动力学特征分析及应用研究[D].兰州：兰州理工大学，2022.doi:10.2720b/d.cnki.gg8gu.2022.001450 PENG Jiankui.Electronzagnetic Induction Neuron Model Under the Dynamic Characteristics Analysis and Application Research[D].Lanzhou:Lanzhou University of Technology,2022.
  • [30] 程万朋.一类神经元系统的同步控制及其在保密通信中的应用[D].兰州：兰州交通大学，2021.doi:10.27205/d.cnki.gltec.202.000173 CHENG Wanpeng.Type of Neuron System of Synchronous Control and Its Application in Secret Communication[D].Lanzou:Lanzhou Jiaotong University,2021.

版权所有 2013-2021 河北师范大学学报编辑部 地址：河北省石家庄市南二环东路20号

邮编：050024 电话：0311-80786360 技术支持：载驰科技