文献类型：期刊文献

中文题名：一类随机惯性时滞神经网络的稳定性

英文题名：Stability of stochastic and intertial neural networks with time delays

作者：章月红[1];刘伟[1];蒋望东[1]

机构：[1]绍兴文理学院元培学院数学教研部,浙江绍兴312000

年份：2020

卷号：35

期号：1

起止页码：83

中文期刊名：高校应用数学学报：A辑

收录：CSTPCD、、北大核心2017、北大核心

基金：浙江省高等教育教学改革研究项目(JG20160261);教育部产学合作协同育人项目(201801123017);绍兴市高等教育教学改革研究项目(SXSJG201833)。

语种：中文

中文关键词：随机惯性时滞神经网络;同胚映射;微分算子;全局渐近稳定;指数稳定

外文关键词：stochastic intertial neural networks with time delays;homeomorphic mapping;differential operator;global asymptotic stability;exponential stability

中文摘要：研究一类随机惯性时滞神经网络稳定性问题.通过引入适当变量变换将二阶微分系统转换为一阶微分系统,利用同胚映射,Ito公式和微分算子,构造恰当的Lyapunov函数和采用递推归纳,给出其系统平衡点存在唯一及全局渐近稳定和解指数稳定判定的充分条件,最后通过数值模拟例子说明所得理论结果的正确性.

外文摘要：The stability problem of a class of stochastic inertia neural networks with time delays is studied.By introducing appropriate variable transformation,the second-order differential system is transformed into a first-order differential system,using the homeomorphic mapping,Ito formula and differential operator,constructing the appropriate Lyapunov function and using recursive induction,the sufficient conditions for the existence of the system equilibrium point and the global asymptotic stability and the solution exponential stability are given.Finally,the correctness of the theoretical results is illustrated by numerical simulation examples.