Stability of equilibria of a nonlinear delay differential equation is investigated under stochastic perturbations. The use of Stiltjes integrals allows to consider both discrete and distributed delays in the investigated equation. Obtained conditions of stability in probability are formulated in terms of linear matrix inequalities. The proposed method of investigation can be applied to a number of very popular in research mathematical models such as Mackey–Glass model, neoclassical growth model and e‐commerce model, Nicholson's blowflies equation, mosquito and glassy‐winged sharpshooter populations, SIR epidemic model, social epidemic models, and many similar other mathematical models which can be considered as particular cases of the investigated nonlinear equation.

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关于非线性随机时滞微分方程稳定性研究的一种方法

研究了随机扰动下非线性时滞微分方程平衡的稳定性。使用Stiltjes积分可以在研究的方程中同时考虑离散和分布式延迟。根据线性矩阵不等式表述获得的概率稳定性条件。拟议的调查方法可以应用到许多非常流行的研究数学模型中，例如Mackey-Glass模型，新古典增长模型和电子商务模型，Nicholson的blow蝇方程，蚊子和玻璃翅神枪手种群，SIR流行病模型，社会流行病模型，以及许多其他类似的数学模型，可以将其视为所研究的非线性方程的特殊情况。