非线性系统
数学
平衡点
随机微分方程
二次方程
微分方程
白噪声
理论(学习稳定性)
时滞微分方程
指数函数
应用数学
指数稳定性
控制理论(社会学)
数学分析
物理
计算机科学
统计
机器学习
量子力学
人工智能
几何学
控制(管理)
摘要
The nonlinear delay differential equation with exponential and quadratic nonlinearities is considered. It is assumed that the equation is exposed to stochastic perturbations of the white noise type, which are directly proportional to the deviation of the system state from the equilibrium point. Sufficient conditions for stability in probability of the zero and positive equilibriums of the considered system under stochastic perturbations are obtained. The research results are illustrated by numerical simulations. The proposed investigation procedure can be applied for arbitrary nonlinear stochastic delay differential equations with an order of nonlinearity higher than one. Copyright © 2016 John Wiley & Sons, Ltd.
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