电磁效应下耦合时滞神经元动力学分析  

Dynamic analysis of coupled neurons with time delay under electromagnetic effect

作　　者：何沛妍 杨丽新 党元辰 顾梓玉 HE Pei-yan;YANG Li-xin;DANG Yuan-chen;GU Zi-yu(College of Mathematics and Data Science,Shaanxi University of Science and Technology,Xi an 710021,China)

机构地区：[1]陕西科技大学数学与数据科学学院,陕西西安710021

出　　处：《东北师大学报（自然科学版）》2023年第4期96-104,共9页Journal of Northeast Normal University(Natural Science Edition)

基　　金：国家自然科学基金资助项目(11702195).

摘　　要：考虑神经元内外电磁场分布的变化和时滞的存在,提出一个新的耦合FitzHugh-Nagumo(FHN)神经元模型,并研究了时滞和电流刺激对该神经元模型稳定性的影响.首先,在平衡点处分析该模型的稳定性,判断Hopf分岔的存在性,得到临界时滞的值;其次,将中心流形定理和规范型理论相结合,对临界时滞处存在的周期解进行讨论.通过数值模拟,调整时滞的取值和电流刺激的施加方式,发现在临界时滞处,该神经元系统失稳,当对系统施加一定程度的电流刺激时,该神经元系统从周期放电模式转化为静息状态,系统的稳定性恢复.结果表明,电流刺激可以调控时滞耦合神经元系统的动力学行为,从而进一步改善该系统的稳定性.This paper proposes a new coupled FitzHugh-Nagumo(FHN)neuron model,changes of electromagnetic field distribution inside and outside neurons and existence of time delay are considered,and the effects of time delay and current stimulation on the stability of the neuron model are studied.Firstly,the stability of the model is analyzed at the equilibrium point,the existence of Hopf bifurcation is judged,and the value of critical delay is obtained.Secondly,the periodic solution at the critical time delay is discussed by combining the center manifold theorem and the normal form theory.Through numerical simulation,adjusting the value of time delay and the way of current stimulation,it is found that the neuron system is unstable at the critical time delay.When a certain degree of current stimulation is applied to the system,the neuron system is transformed from periodic discharge mode to resting state,and the stability of the system is restored.The results show that current stimulation can regulate the dynamic behavior of the delayed coupled neuron system,thus further improving the stability of the system.

关 键 词：FHN神经元 时滞 HOPF分岔 电流刺激 

分 类 号：O441[理学—电磁学]