含有离散时滞及分布时滞分数阶神经网络的渐近稳定性分析  

Asymptotic Stability Analysis of Fractional Neural Networks With Discrete Delays and Distributed Delays

作　　者：刘健 张志信[1] 蒋威[1] LIU Jian;ZHANG Zhixin;JIANG Wei(School of Mathematical Sciences,Anhui University,Hefei 230601,P.R.China)

机构地区：[1]安徽大学数学科学学院,合肥230601

出　　处：《应用数学和力学》2020年第6期646-657,共12页Applied Mathematics and Mechanics

基　　金：国家自然科学基金(11371027,11471015,11601003);安徽省自然科学基金(1608085MA12)。

摘　　要：研究了含有离散时滞及分布时滞的分数阶神经网络在Caputo导数意义下的渐近稳定性问题.通过构造Lyapunov函数和利用分数阶Razumikhin定理给出了含有离散时滞和分布时滞的分数阶神经网络渐近稳定性的充分条件,并给出4个例子验证了定理条件的有效性.The asymptotic stability of fractional⁃order neural networks with discrete delays and distributed delays in the sense of Caputo derivatives was studied.Through construction of the Lyapunov function and with the fractional Razumikhin theorem,sufficient conditions for asymp⁃totic stability of fractional⁃order neural networks with discrete and distributed delays were giv⁃en,and 4 examples were given to illustrate the validity of the proposed theorem conditions.

关 键 词：分数阶神经网络 时滞 渐近稳定性 分数阶Razumikhin方法 LYAPUNOV函数 

分 类 号：O175.15[理学—数学]