单向耦合FitzHugh-Nagumo神经元的滞后同步研究  

The Study for Lag Synchronization between Two Fitzhugh-Nagumo Neurons with Unidirectional Coupling

作　　者：袁韦欣 镇斌[1] 徐鉴[2] Yuan Weixin;Zhen Bin;Xu Jian(School of Environment and Architecture,University of Shanghai for Science and Technology,Shanghai 200093,China;School of Aerospace Engineering and Applied Mechanics,Tongji University,Shanghai 200092,China)

机构地区：[1]上海理工大学环境与建筑学院,上海200093 [2]同济大学航空航天与力学学院,上海200092

出　　处：《动力学与控制学报》2023年第8期19-23,共5页Journal of Dynamics and Control

基　　金：国家自然科学基金面上项目(11672185)。

摘　　要：本文提出一种新的研究思路,将两个单向耦合的FitzHugh-Nagumo神经元之间的滞后同步视为一种特殊的广义同步,通过辅助系统方法来获得滞后同步发生的条件.首先建立原响应系统的辅助系统,将原系统中驱动系统和响应系统的滞后同步问题转换为响应系统与辅助系统之间的误差系统原点稳定问题.通过拉普拉斯变换方法,将原本用微分方程表示的误差系统等效为Volterra积分方程表示,而后利用积分方程理论中的逐次逼近方法解析地得到原误差系统原点稳定性条件.本文给出的滞后同步判据与信号传送中的时间滞后量大小无关,数值模拟验证了本文提出判据的有效性.In this paper,a new method is proposed based on the auxiliary system approach to investigate lag synchronization between two identical FitzHugh-Nagumo(FHN)neurons with unidirectional coupling.The lag synchronization can be achieved if the synchronization error system between the response and auxiliary systems has an asymptotically stable origin.Different from other studies,the synchronization error system is converted into a set of Volterra integral equations according to the Laplace transform.By using the successive approximation method in the theory of integral equations,an analytical criterion for the detection of lag synchronization between two FHN neurons is obtained.The value of the time delay in transmission has no relation to the lag synchronization condition,which has been verified by numerical simulations for the original system.

关 键 词：FitzHugh-Nagumo神经元 时滞 滞后同步 广义同步 单向耦合 

分 类 号：O317.2[理学—一般力学与力学基础]