一维离散型核函数的神经场稳态解的研究  

Research on the stationary solution to one-dimensional neural field with discrete kernel function

作　　者：况发伦 杨慕容 金德泉[1] KUANG Fa-lun;YANG Mu-rong;JIN De-quan(College of Mathematics and Information Science, Guangxi University, Nanning 530004, China)

机构地区：[1]广西大学数学与信息科学学院,广西南宁530004

出　　处：《广西大学学报（自然科学版）》2020年第4期906-910,共5页Journal of Guangxi University（Natural Science Edition）

基　　金：国家自然科学基金资助项目(11661010);广西重大研究课题项目(桂科AB18126007,桂科AB17292095)。

摘　　要：为研究交互核为离散型核函数的Amari动力神经场的稳态解的存在性和相关性质,给定阈值函数为单位阶跃函数,将核函数具体化,通过数学证明得出了带有离散型核函数的神经场方程稳态解的存在性,同时给出了在特定条件下,局部解半径的求法,并分析了局部解的稳定性。In order to study the existence and related properties of stationary solutions of Amari dynamic neural field with discrete kernel function,the threshold function is given as a unit step function,and the kernel function is embodied.The existence of stationary solutions of neural field equations with discrete kernel functions is proved mathematically.At the same time,the method of finding the radius of local solution under certain conditions is given,and the stability of local solution is analyzed.

关 键 词：神经场 稳态解 交互核 阈值函数 

分 类 号：O29[理学—应用数学]