具有ReLU函数的动力神经场方程稳定解的存在性  

Existence of stationary solution of Amari dynamical neural field with ReLU function

作　　者：秦子雁 陈芃合 金德泉[1] QIN Zi-yan;CHENG Peng-he;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）》2021年第1期231-235,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：为进一步探索动力神经场的相关性质,将单调递增但是无界的ReLU函数作为阈值函数运用在一维的Amari动力神经场中,这与将单调有界的阶跃函数或Sigmoid型函数作为阈值函数的传统动力神经场研究不同。在不考虑输入,且相互作用核为高斯函数的情况下,对3种不同的稳定解进行研究,得出Amari动力神经场稳定解的存在条件和相关性质。In order to study the properties of dynamical neural field,the monotonically increasing and unbounded ReLU functions are applied as the threshold function to one-dimensional Amari dynamical neural field,which is different from traditional researches on Amari dynamical neural field that took the monotonically increasing but bounded function,such as step function or Sigmoid function,as the threshold function.Under the condition that there is no consideration of input and taking the Gaussian function as interaction kernel,three different types of stationary solutions are studied,and the existing conditions and relevant properties of the stationary solutions are obtained.

关 键 词：Amari动力神经场 稳定解 ReLU函数 高斯函数 

分 类 号：O29[理学—应用数学]