一类忆阻神经元的电活动多模振荡及Hamilton 能量反馈控制

安新磊; 张莉

doi:10.6052/0459-1879-20-035

一类忆阻神经元的电活动多模振荡及Hamilton 能量反馈控制

doi: 10.6052/0459-1879-20-035

安新磊^*†2), ,,
张莉^**

^*兰州交通大学数理学院, 兰州 730070
^†兰州理工大学电气工程与信息工程学院, 兰州 730050
^**兰州工业学院基础学科部, 兰州 730050

基金项目: 1)国家自然科学基金(11962012);中国博士后科学基金(2018M633649XB)

详细信息

通讯作者:
安新磊

中图分类号: O415.5
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出版历程
- 收稿日期: 2020-02-11
- 刊出日期: 2020-08-10

MULTI-MODE OSCILLATIONS AND HAMILTON ENERGY FEEDBACK CONTROL OF A CLASS OF MEMRISTOR NEURON

An Xinlei^{*†2)
, ,},
Zhang Li^**

^*School of Mathematics and Physics,Lanzhou Jiaotong University, Lanzhou 730070, China
^†College of Electrical and Information Engineering,Lanzhou University of Technology,Gansu Lanzhou 730050, China
^**The Basic Courses Department of Lanzhou Institute of Technology,Gansu Lanzhou 730050, China

摘要

摘要: 根据法拉第电磁感应定律,在离子穿越细胞膜或者在外界电磁辐射下,细胞内外的电生理环境会产生电磁感应效应,继而会影响神经元的电活动行为. 基于此,本文考虑电磁感应影响下的 Hindmarsh-Rose (HR) 神经元模型,研究了其混合模式振荡放电特征,并设计一个 Hamilton 能量反馈控制器,将其控制到不同的周期簇放电状态. 首先,通过理论分析发现磁通 HR 神经元系统的 Hopf 分岔使其平衡点的稳定性发生了改变,并产生极限环,进而研究了 Hopf 分岔点附近膜电压的放电特征. 基于双参数数值仿真发现该系统具有丰富的分岔结构,在不同的参数平面上存在倍周期分岔、伴有混沌的加周期分岔、无混沌的加周期分岔以及共存的混合模式振荡. 最后,为了有效控制膜电压的混合模式振荡,利用亥姆霍兹理论计算出磁通 HR 神经元系统的 Hamilton 能量函数并设计 Hamilton 能量反馈控制器,通过数值仿真分析了膜电压在不同反馈增益下的簇放电状态,发现该控制器能够有效地控制膜电压到不同的周期簇放电模式. 本文的研究结果为探究电磁感应下神经元的分岔结构及其能量控制领域提供了有用的理论支撑.
- 磁通 HR 神经元 /
- 双参数分岔分析 /
- 多模振荡 /
- Hamilton 能量控制 /
- 周期簇放电
Abstract: According to Faraday's electromagnetic induction law, the electrophysiological environment in and out the cell will produce electromagnetic induction effects in the case of ions penetrating the cell membrane or in the case of being exposed to external electromagnetic radiation, which will affect the electrical activity behavior of neural systems. Based on this principle, this paper studies the mixed-mode oscillation discharge characteristics of the Hindmarsh-Rose(HR) neuron model (here we call it as magnetic flux HR neuron model) with the influence of electromagnetic induction, and designs a Hamilton energy feedback controller to manage the mode to different periodic cluster discharge states. First, through theoretic analysis, it is found that the stability of equilibrium point in the magnetic flux HR neuron model is changed by the occurrence of Hopf bifurcation in the magnetic flux HR neuron model and a limit cycle is generated. Besides, some discharge characteristics of the membrane voltage near the Hopf bifurcation point are also discussed in detail. Then, it is also displayed there are abundant bifurcation structures in the magnetic flux HR neuron model based on the two-parameter numerical simulations, which includes multi-period bifurcation, period-adding bifurcation with chaos, period-adding bifurcation without chaos and co-existing mixed-mode oscillations in different initial conditions. At last, with the purpose of controlling the mixed-mode oscillation of membrane voltage, the Hamilton energy function is calculated by utilizing the Helmholtz theorem, and a Hamilton energy feedback controller is designed further. Additionally, it can be seen that the controller can effectively control the membrane voltage in different periodic clustering discharge modes, with the analysis of the discharge states of membrane voltage under different feedback gains in view of the numerical simulation. The results of this paper provide a useful theoretical support for the study of bifurcation structure in artificial neuron system under electromagnetic induction and the field of energy control related to the neurons.
- magnetic flux HR neuron /
- bifurcation analysis with two-parameter /
- multi-mode oscillations /
- Hamilton energy control /
- periodic bursting

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参考文献(1)

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