一类变时滞复数Cohen-Grossberg神经网络的动态行为分析  

Dynamical Behavior Analysis of a Class of Complex-Valued Neural Networks With Time-Varying Delays

作　　者：徐晓惠[1,2] 宋乾坤 张继业[4] 施继忠[5] 赵玲[2] 

机构地区：[1]西华大学流体及动力机械教育部重点实验室,成都610039 [2]西华大学汽车测控与安全四川省重点实验室,成都610039 [3]重庆交通大学数学与统计学院,重庆400074 [4]牵引动力国家重点实验室(西南交通大学),成都610031 [5]浙江师范大学工学院,浙江金华321004

出　　处：《应用数学和力学》2017年第12期1389-1398,共10页Applied Mathematics and Mechanics

基　　金：国家自然科学基金(11402214;51375402;11572264;61773004);四川省青年科技创新研究团队(2017TD0035;2017TD0026;2015TD0021;2016HH0010);四川省教育厅自然科学重点项目(17ZA0364);浙江省自然科学基金(LY14E08006);教育部"春晖计划"合作科研项目(Z2014075);重庆创新团队项目(CXTDX201601022)~~

摘　　要：研究了一类具有变时滞的复数域Cohen-Grossberg神经网络平衡点的动态行为.在假定激活函数满足Lipschitz条件并且放大函数只满足具有下界的情况下,利用M矩阵和同胚映射原理,得到了确保该系统平衡点的存在性和唯一性的充分条件.基于矢量Lyapunov函数法和不等式技术,得到了确保该系统平衡点的模指数稳定性的判据.该判据形式简单,在实际应用时便于检验.该文所取得的研究成果推广了现有结论.最后通过给出一个数值算例和仿真结果验证了所得结论的正确性和可行性.The dynamical behavior of a class of complex-valued Cohen-Grossberg neural networks with time-varying delays was studied. It was supposed that the activation functions satisfied the Lipschitz condition and the amplification functions had only the lower bounds. The sufficient conditions ensuring the existence and the uniqueness of the equilibrium point of the system were acquired by means of the M matrix and the homeomorphic mapping. Furthermore,based on the vector Lyapunov function method and the inequality technique the criteria were obtained to judge the mode exponential stability of the equilibrium point of the system. The form of the obtained sufficient conditions is simple,and is easy to be verified in practice. The presented results generalize the existing ones. Finally a numerical example through simulation was given to verify the correctness and feasibility of the obtained results.

关 键 词：COHEN-GROSSBERG神经网络 复数域 模稳定性 指数稳定性 变时滞 矢量Lyapunov函数法 

分 类 号：O175[理学—数学]