一类带有时滞的模糊分数阶广义神经网络的定性分析  

Qualitative Analysis of a Class of Fuzzy Fractional-Order Generalized Neural Networks with Time Delays

作　　者：饶绍斌 吕小俊 聂家升 郝冰[2] RAO Shaobin;LV Xiaojun;NIE Jiasheng;HAO Bing(College of Applied Technology,Soochow University,Suzhou 215325,China;College of Oxbridge,Kunming University of Science and Technology,Kunming 650106,China)

机构地区：[1]苏州大学应用技术学院,江苏苏州215325 [2]昆明理工大学津桥学院,云南昆明650106

出　　处：《贵州大学学报（自然科学版）》2023年第5期15-22,共8页Journal of Guizhou University:Natural Sciences

基　　金：云南省教育厅科学研究基金资助项目(2022J1097)。

摘　　要：一阶半线性微分方程的欧拉差分在过去十几年里得到了迅速的发展,并得出了一些很好的结果。因此,各种欧拉差分方法已成为非常重要的研究课题。本文主要研究了带有时滞的模糊分数阶广义神经网络,利用分数阶微积分中的常数变分公式,建立了一类具有时滞的模糊分数阶广义神经网络的差分模型,并对该差分模型进行了定性分析。首先,利用压缩映射原理证明了差分模型有界解和平衡点的存在唯一性;其次,利用不等式放缩技巧和反证法,证明了差分模型解的指数稳定性。本文的研究成果,一方面可以丰富这类神经网络的理论成果;二方面可以拓展这类神经网络的应用范畴。Euler difference of first order semilinear differential equations has been developed rapidly in the last decade and some good results have been obtained.Therefore,various Euler difference methods have become very important research topics.This paper mainly studies fuzzy fractional-order generalized neural networks with time delay.A kind of difference model of fractional-order generalized neural network with time delay is established using the constant variational formula in fractional-order calculus.Firstly,the existence and uniqueness of the bounded solution and the equilibrium point of the difference model are proved by the compression mapping principle.Secondly,the exponential stability of the solution of the difference equation is proved by means of inequality reduction technique and inverse proof.The research results of this paper can enrich the theoretical achievements of this kind of neural networks and expand their application scope.

关 键 词：CAPUTO分数阶导数 广义神经网络 差分方程 平衡点 指数稳定 

分 类 号：O175.13[理学—数学]