河北师范大学学报—

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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
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电场下HR神经元的分岔分析及其同步

祁慧敏¹

张莉²

安新磊¹

肖冉¹

1. 兰州交通大学数理学院, 甘肃兰州 730070;
2. 兰州工业学院基础学科部, 甘肃兰州 730050
DOI： 10.13763/j.cnki.jhebnu.nse.202102003

Bifurcation Analysis and Synchronization of HR Neurons Under Electric Field

QI Huimin¹, ZHANG Li², AN Xinlei¹, XIAO Ran¹

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摘要/Abstract

摘要：

应用数值仿真与自适应同步控制方法，分析了Hindmarsh-Rose（HR）神经元模型在外加电场的影响下产生的复杂动力学行为. 在基于数值模拟得到的双参数图像中了解到该系统具有倍周期分岔、加周期分岔模式以及"梳状"的混沌结构.在此基础上，运用Lyapunov稳定性理论以及未知参数自适应律设计出满足同步条件的自适应控制器，并通过数值仿真验证得出：该控制器具有较好的稳定性与自适应性. 所得研究成果可以为在电场作用下神经元及其复杂网络的动力学特性的研究提供参考.

Abstract：

The complex dynamic behavior of Hindmarsh-Rose(HR) neuron model under an applied electric field was analyzed in detail by using numerical simulation and adaptive synchronous control. The two-parameter images obtained by numerical simulation show that the system has period-doubling bifurcation, period-adding bifurcation modes and "comb" chaotic structure.On this basis, by using Lyapunov stability theory and the adaptive law of unknown parameters,an adaptive controller satisfying the synchronization condition was designed, and numerical simulation was carried out to verify that the controller has a good stability and adaptability. The results in this paper will provide a useful reference for studying the dynamic characteristics of neurons and their complex networks under the action of electric fields.

关键词

关键词： HR神经元模型 ; 双参数分岔分析 ; 加周期分岔 ; 混沌自适应同步

Key words： HR neuron model ; bifurcation analysis with two parameters ; add periodic bifurcation ; chaotic adaptive synchronization

参考文献 14

[1] LYU M,WANG C,REN G,et al.Model of Electrical Activity in a Neuron Under Magnetic Flow Effect[J].Nonlinear Dynamics,2016,85(3):1479-1490.
[2] 乔帅,张莉,安新磊,等.电磁辐射下HR神经元模型的分岔分析[J].河北师范大学学报(自然科学版),2019,43(4):122-128.doi:10.13763/j.cnki.jhebnu.nse.2019.04.005 QIAO Shuai,ZHANG Li,AN Xinlei,et al.Bifurcation Analysis of HR Neuron Model Under Electromagnetic Radiation[J].Journal of Hebei Normal University (Natural Science),2019,43(4):122-128.
[3] 李佳佳,吴莹,独盟盟,等.电磁辐射诱发神经元放电节律转迁的动力学行为研究[J].物理学报,2015(3):224-230. LI Jiajia,WU Ying,DU Mengmeng,et al.Study on the Dynamic Behavior of Neuronal Firing Rhythm Transition Induced by Electromagnetic Radiation[J].Acta Phys Sin,2015(3):224-230.
[4] MA J,ZHANG G,HAYAT T,et al.Model Electrical Activity of Neuron Under Electric Field[J].Nonlinear Dynamics,2015,58(12):2038-2045.doi:10.1007/s11431-015-9561-6
[5] 张薇,安新磊,乔帅,等.e-HR神经元模型分岔分析与隐藏放电控制[J].河北师范大学学报(自然科学版),2020,44(2):123-129.doi:10.13763/j.cnki.jhebuu.nse.2020.02.005 ZHANG Wei,AN Xinlei,QIAO Shuai,et al.Bifurcation Analysis and Hidden Discharge Control of e-HR Neuron Model[J].Journal of Hebei Normal University (Natural Science),2020,44(2):123-129.
[6] 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.
[7] WU F,WANG C,JIN W,et al.Dynamical Responses in a New Neuron Model Subjected to Electromagnetic Induction and Phase Noise[J].Physica A:Statistical Mechanics and Its Applications,2017,469:81-88.
[8] BAO H,HU A,LIU W,et al.Hidden Bursting Firings and Bifurcation Mechanisms in Memristive Neuron Model with Threshold Electromagnetic Induction[J].IEEE Transactions on Neural Networks and Learning Systems,2019,25(4):2162-2171.doi:10.1109/TNNLS.2019.2905137
[9] WANG C,TANG J,MA J.Minireview on Signal Exchange Between Nonlinear Circuits and Neurons via Field Coupling[J].The European Physical Journal Special Topics,2019,228(10):1907-1924.
[10] 谭安杰,韦笃取,覃英华.电磁场耦合忆阻神经网络的放电模式及同步行为研究[J].广西师范大学学报(自然科学版),2020,38(1):107-113.doi:10.16088/j.issn.1001-6600.2020.01.014 TAN Anjie,WEI Duqu,QIN Yinghua.Study on Discharge Mode and Synchronous Behavior of Electromagnetic Field Coupled Yi-retard Neural Network[J].Journal of Guangxi Normal University (Natural Science),2020,38(1):107-113.
[11] HETTIARACHCHI I T,LAKSHMANAN S,BHATTI A,et al.Chaotic Synchronization of Time-delay Coupled Hindmarsh-rose Neurons via Nonlinear Control[J].Nonlinear Dynamics,2016,86(2):1249-1262.
[12] 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. WU Kaijun,WANG Chunli,SHAN Yazhou,et al.Synchronization of Chemical Synaptic Coupling Neuron System Under Noise[J].Journal of Jilin University (Engineering Science),2017,47(5):1554-1560.
[13] 王红梅,安新磊,乔帅,等.e-HR神经元模型分岔分析与同步控制[J].山东大学学报(理学版),2020,55(9):10-18.doi:10.6040/j.issn.1671-9352.0.2019.795 WANG Hongmei,AN Xinlei,QIAO Shuai,et al.e-HR Neuron Model Bifurcation Analysis with the Synchronous Control[J].Journal of Shandong University (Natural Science),2020,55(9):10-18.
[14] WU K,WANG T,WANG C,et al.Study on Electrical Synapse Coupling Synchronization of Hindmarsh-Rose Neurons Under Gaussian White Noise[J].Neural Computing & Applications,2016(3):1-11.