| 一类变时滞复数Cohen-Grossberg神经网络的动态行为分析 |
| |
| 引用本文： | 徐晓惠,宋乾坤,张继业,施继忠,赵玲.一类变时滞复数Cohen-Grossberg神经网络的动态行为分析[J].应用数学和力学,2017,38(12):1389-1398. |
| |
| 作者姓名： | 徐晓惠 宋乾坤 张继业 施继忠 赵玲 |
| |
| 作者单位： | 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 |
| |
| 基金项目： | 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.
|
| 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 |
| 收稿时间： | 2017-01-11 |
Dynamical Behavior Analysis of a Class of Complex-Valued Neural Networks With Time-Varying Delays |
| |
| Abstract: | 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. |
| |
| Keywords: | |
| 本文献已被 CNKI 等数据库收录！ |
| 点击此处可从《应用数学和力学》浏览原始摘要信息 |
| 点击此处可从《应用数学和力学》下载免费的PDF全文 |
