一维Hopfield神经网络模型的多稳态分析  

Multistable analysis for one dimensional Hopfield neural networks

作　　者：宿娟[1] 何志蓉[2] 

机构地区：[1]成都师范学院数学系,成都610044 [2]四川大学数学学院,成都610064

出　　处：《四川大学学报（自然科学版）》2016年第2期260-264,共5页Journal of Sichuan University(Natural Science Edition)

基　　金：国家自然科学基金(61202045);成都师范学院科研基金(CS15ZB04)

摘　　要：本文讨论一维Hopfield神经网络模型的多稳态问题.当模型所含S型激活函数没有有界性限制时,本文首先讨论了模型平衡点的存在性,并进一步给出了模型取得一个,二个,或三个平衡点的参数条件以及每个平衡点的稳定性.然后本文研究了模型在参数所有取值情况下的平衡点个数及其稳定性.最后,通过两个实例及其数值模拟说明了结果的有效性.This paper focuses on multistable analysis of one dimensional Hopfield neural networks,whose sigmoid activation function may not be bounded.Firstly,the condition for the existence of equilibria is established,the conditions for exactly 1,2,or 3equilibria and their respectively stability are proposed with some constraints for network parameters.Then the corresponding results about the equilibria features are supplemented in the remaining cases for the parameters.Thus,we obtain the relationships between all the different values of the parameters and the number of equilibria as well as their stability.Finally,by employing bounded and unbounded activation functions,two examples and numerical simulations are used to illustrate the theory developed in this paper.

关 键 词：HOPFIELD神经网络 多稳态 激活函数 渐近稳定 平衡点 

分 类 号：O175[理学—数学]