About one method of stability investigation for nonlinear stochastic delay differential equations. (8th February 2021) - Shaikhet, Leonid
Abstract: 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.