分数阶时滞神经网络渐近稳定与同步分析  

Asymptotical Stability and Synchronization of Fractional Delayed Neural Networks

作　　者：刘雪铃 黄静 LIU Xueling;HUANG Jing(Department of Electronic and Information Engineering,Bozhou College,236800,Bozhou,Anhui,China)

机构地区：[1]亳州学院电子与信息工程系,安徽亳州236800

出　　处：《淮北师范大学学报（自然科学版）》2023年第1期16-20,共5页Journal of Huaibei Normal University：Natural Sciences

基　　金：安徽省省级质量工程项目(2019mooc374);安徽省高校自然科学研究项目(KJ2021A1150);安徽省自然科学基金项目(2022AH052415)。

摘　　要：针对带分布时滞的分数阶神经网络模型解的存在唯一性、渐近稳定性以及同步问题,首先利用Banach压缩映像原理,证明该系统平衡点的存在唯一性。然后通过构造恰当的Lyapunov泛函,得到该系统渐近稳定的充分条件。通过设计一个自适应控制器,得到该系统渐近同步的判定依据。最后利用数值仿真,验证所得结果的有效性与可行性。The existence and uniqueness of the solution,asymptotical stability and synchronization of fractional neural networks with distributed delay was considered. Firstly,the existence and uniqueness of equilibrium point was proposed by using the contraction mapping principle. Secondly,by constructing an appropriate Lyapunov functional,an asymptotical stability criteria of the system was obtained. Thirdly,an asymptotical synchronization criterion was obtained by an adaptive controller. Finally,numerical examples were used to check the validity and feasibility of the proposed results.

关 键 词：分数阶神经网络 分布时滞 存在唯一性 渐近稳定与同步 

分 类 号：O29[理学—应用数学]