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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2022, Vol. 39 ›› Issue (1): 159-170.doi: 10.3969/j.issn.1005-3085.2022.01.012

• • 上一篇    

磁通 e-HR 神经元模型的放电行为及同步控制

马  杰,   高  洁,   独盟盟,   杨丽新   

  1. 陕西科技大学文理学院，西安 710021
  • 出版日期:2022-02-15 发布日期:2022-04-15
  • 通讯作者: 杨丽新 E-mail: yanglixin@sust.edu.cn
  • 基金资助:
    国家自然科学基金 (11702195).

Discharge Behavior Analysis and Control Synchronization of Magnetic Flux e-HR Neuron Model

MA Jie,   GAO Jie,   DU Mengmeng,   YANG Lixin   

  1. School of Art and Science, Shaanxi University of Science and Technology, Xi'an 710021
  • Online:2022-02-15 Published:2022-04-15
  • Contact: L. Yang. E-mail address: yanglixin@sust.edu.cn
  • Supported by:
    The National Natural Science Foundation of China (11702195).

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摘要：

以 e-HR 神经元模型为基础，在考虑外界电磁场对神经元膜电位变化的影响下构建磁通 e-HR 神经元模型。首先，利用盛金公式来求得磁通 e-HR 神经元模型平衡点个数以及对其平衡点稳定性进行了研究，同时进一步利用分岔理论找出系统发生分岔时的条件。其次，通过改变外加刺激电流以及磁通反馈增益，发现神经元呈现出簇放电、周期放电等多种放电模式。此时平衡点的不稳定状态对应为神经元放电模式；稳定状态对应静息模式，即不放电模式。最后，基于Lyapunov稳定理论设计自适应控制器，通过理论分析和数值仿真证明了控制器的有效性与可行性。

关键词: e-HR 神经元, Hopf 分岔, 放电, 同步

Abstract:

Based on the e-HR neuron model, a magnetic flux e-HR neuron model is constructed under the influence of external electromagnetic fields with membrane potential changes. Firstly, the Shengjin formula is used to obtain the number of equilibrium points of the magnetic flux e-HR neuron model and the stability of the equilibrium points, and at the same time the bifurcation theory is further used to find out the conditions for the bifurcation of the system. Secondly, by changing the applied stimulation current and the magnetic flux feedback gain, it is found that the neurons present a variety of firing modes such as cluster firing and periodic firing. What's more, the unstable state of the equilibrium point corresponds to the neuronal firing mode; the steady state corresponds to the resting mode, that is, the non-discharge mode. Finally, an adaptive controller is designed based on the Lyapunov stability theory, and the effectiveness and feasibility of the controller is proved through theoretical analysis and numerical simulation.

Key words: e-HR neuron, Hopf bifurcation, firing, synchronization

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