带马氏切换和时变时滞的随机神经网络的依分布渐近稳定性  

Asymptotic Stability in Distribution of Stochastic Neural Networks with Markovian Switching and Time-Varying Delays

作　　者：王玉春[1,2] 王莉 WANG Yu-chun;WANG Li(School of Liberal and Science,Suqian University,Suqian Jiangsu 223800,China;School of Mathematics,China University of Mining and Technology,Xuzhou Jiangsu 221116,China)

机构地区：[1]宿迁学院文理学院,江苏宿迁223800 [2]中国矿业大学数学学院,江苏徐州221116

出　　处：《淮阴师范学院学报（自然科学版）》2023年第4期296-301,共6页Journal of Huaiyin Teachers College;Natural Science Edition

基　　金：国家自然科学基金资助项目(61873271)。

摘　　要：考虑到神经网络在实际应用中常会伴有时滞现象,研究了一类带马氏切换的随机神经网络在时变时滞下按分布的渐近稳定性.根据模型的特点,并结合按分布渐近稳定性的充分条件,构造了Lyapunov函数,利用广义的Ito公式、不等式放缩技巧,得到了系统的稳定性充分条件.最后利用数值模拟,验证了理论结果的正确性.Considering that neural networks often have delays in practical applications,the asymptotic stability in distribution of stochastic neural networks with Markov switching under time-varying delays is studied.According to the characteristics of the model equation and the sufficient condition of asymptotic stability in distribution,the Lyapunov function is constructed,and the corresponding sufficient condition of stability of the system is obtained by means of generalized Ito formula calculation and inequality magnifying technique.Finally,a numerical example is given to verify the feasibility of the results.

关 键 词：马氏切换 时变时滞 随机神经网络 依分布渐近稳定 LYAPUNOV函数 

分 类 号：O175[理学—数学]