分数阶Hopfield神经网络的Hyers-Ulam-Rassias稳定性判定准则  

A Discriminant Criterion of Hyers-Ulam-Rassias Stability of Fractional Order Hopfield Neural Networks

作　　者：冯明晗 刘孝磊 毛凯 FENG Ming-han;LIU Xiao-lei;MAO Kai(Naval Aviaion School,Naval Aeronautical University,Yantai 264100,China)

机构地区：[1]海军航空大学航空基础学院,山东烟台264100

出　　处：《辽宁大学学报(自然科学版)》2025年第1期71-78,共8页Journal of Liaoning University:Natural Sciences Edition

基　　金：海军航空大学青年基金项目(H3202308005)。

摘　　要：本文旨在研究分数阶Hopfield神经网络(Fractional order Hopfield neural networks,FHNN)的Hyers-Ulam-Rassias稳定性.利用Mittag-Leffler函数和Gronwall估计定理,给出了当神经元激活函数满足Lipschitz条件时,神经网络满足Hyers-Ulam-Rassias稳定性的一个充分条件,从而提供了一种通过验证自反馈系数矩阵和权重系数矩阵判断神经网络具有Hyers-Ulam稳定性的方法.最后,本文设置满足定理的神经网络系数,利用仿真实验,验证此充分条件的正确性.This article investigates the Hyers-Ulam-Rassias stability of fractional order Hopfield neural networks(FHNN).By utilizing operational properties and estimation theorem of the Mittag-Leffler function and Gronwall inequality,a sufficient condition is given for the Hyers-Ulam-Rassias stability of FHNN when the activation function satisfies the Lipschitz condition.This provides a method for determining the Hyers-Ulam stability of FHNN by verifying the self-feedback coefficient matrix and weight coefficient matrix.Finally,this article sets neural network coefficients that satisfy the conditions of the theorem,and uses simulation experiments to verify the correctness of the theorem.

关 键 词：分数阶Hopfield神经网络 HYERS-ULAM-RASSIAS稳定性 LIPSCHITZ条件 

分 类 号：TP183[自动化与计算机技术—控制理论与控制工程]