一类中立型时滞神经网络的稳定性分析  

Stability analysis of a class of neutral time-delay neural networks

作　　者：田宝单[1] 钱紫舒 徐鑫 Tian Baodan;Qian Zishu;Xu Xin(School of Mathematics and Physics,Southwest University of Science and Technology,Mianyang 621010,China)

机构地区：[1]西南科技大学数理学院,四川绵阳621010

出　　处：《海南大学学报（自然科学版）》2024年第3期244-250,共7页Journal of Hainan University（Natural Science）

基　　金：四川省科技厅应用基础项目(2017JY0336);西南科技大学龙山人才科研支持计划项目(18LZX622);达州市数学与金融研究中心重点项目(SCMF202201)。

摘　　要：对一类时变时滞的中立型神经网络进行研究,首先利用同胚映射定理证明了系统平衡点的存在唯一性,其次通过构造适当的Lyapunov泛函并利用矩阵不等式的技巧得到了系统正平衡点全局渐近稳定的充分条件,最后通过2个数值算例来进一步验证所给条件的可行性和理论的正确性.In the report,a class of neutral neural networks with time-varying delays was analyzed.The homeo⁃morphic mapping theorem was used to prove the existence and uniqueness of the equilibrium point.The appro⁃priate Lyapunov functional was constructed,and the technique of matrix inequalities was used to derive the suffi⁃cient conditions for the global asymptotic stability of the positive equilibrium point.Finally,a numerical exam⁃ple was proposed to verify the feasibility of the conditions and the correctness of the theory.

关 键 词：中立型神经网络 时变时滞 同胚映射 LYAPUNOV泛函 全局渐近稳定性 

分 类 号：O175.13[理学—数学]