一类随机惯性时滞神经网络的稳定性  

Stability of stochastic and intertial neural networks with time delays

作　　者：章月红 刘伟[1] 蒋望东 ZHANG Yue-hong;LIU Wei;JIANG Wang-dong(Department of Mathematics,Yuanpei College of Shaoxing University,Shaoxing 312000,China)

机构地区：[1]绍兴文理学院元培学院数学教研部,浙江绍兴312000

出　　处：《高校应用数学学报（A辑）》2020年第1期83-98,共16页Applied Mathematics A Journal of Chinese Universities(Ser.A)

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)。

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.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.

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 

分 类 号：O175[理学—数学] TP183[理学—基础数学]