具有反应扩散项的变时滞复数域神经网络的指数稳定性  

Exponential Stability of Complex-Valued Neural Networks With Time-Varying Delays and Reaction-Diffusion Terms

作　　者：施继忠[1] 徐晓惠 蒋永华[1] 杨继斌 孙树磊 SHI Jizhong;XU Xiaohui;JIANG Yonghua;YANG Jibin;SUN Shulei(College of Engineering,Zhejiang Normal University,Jinhua,Zhejiang 321004,P.R.China;School of Automobile and Transportation,Xihua University,Chengdu 610039,P.R.China)

机构地区：[1]浙江师范大学工学院,浙江金华321004 [2]西华大学汽车与交通学院,成都610039

出　　处：《应用数学和力学》2021年第5期500-509,共10页Applied Mathematics and Mechanics

基　　金：国家重点研发计划(2018YFB1201603);四川省科技厅重大专项项目(2019ZDZX0002);四川省科技厅项目(2018GZ0110);浙江省自然科学基金(LY18G010009);成都市重大科技创新项目(2019-YF08-00003-GX);四川省重点研发计划(2020YFG0023,2021YFG0071)。

摘　　要：该文研究了一类具有反应扩散项的变时滞复数域神经网络的指数稳定性.首先在假设复数域激活函数可分解的情况下,将该系统分解为相应的实部系统和虚部系统.利用矢量Lyapunov函数法和M矩阵理论,得到了确保该系统平衡状态指数稳定性的充分条件.该条件不含有任何自由变量,相对现有结论具有较低的保守性.最后通过一个数值仿真算例验证了所得结论的正确性.The exponential stability of complex-valued neural networks with time-varying delays and reaction-diffusion terms was studied.Firstly,the addressed systems were separated into their real parts with the complex-valued activation functions assumed to be divided into the real parts and imaginary parts.Secondly,some sufficient conditions for ensuring the exponential stability of the equilibrium states of the systems were established based on the vector Lyapunov function method and the M-matrix theory.The obtained criteria have no free variables and reduced conservatism compared with the existing results.A numerical example proves the correctness of the obtained results.

关 键 词：复数域神经网络 变时滞 反应扩散项 矢量Lyapunov函数法 指数稳定性 

分 类 号：O175.13[理学—数学]