在线阅读 --自然科学版 2021年1期《电场下HR神经元的分岔分析及其同步》
电场下HR神经元的分岔分析及其同步--[在线阅读]
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
起止页码: 39--45页
DOI: 10.13763/j.cnki.jhebnu.nse.202102003
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.

Bifurcation Analysis and Synchronization of HR Neurons Under Electric Field
QI Huimin1, ZHANG Li2, AN Xinlei1, XIAO Ran1
1. College of Mathematics and Physics, Lanzhou Jiaotong University, Gansu Lanzhou 730070, China;
2. Department of Basic Sciences, Lanzhou Institute of Technology, Gansu Lanzhou 730050, China
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.

收稿日期: 2020-08-22
基金项目: 国家自然科学基金(11962012);兰州交通大学研究生教育改革项目(JG201816)

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