高阶非线性混杂随机时滞微分方程的多项式稳定性分析

Analysis on Polynomial Stability of Highly Nonlinear Hybrid Stochastic Delay Differential Equations

研究了高阶非线性混杂随机时滞微分方程的多项式稳定性问题。通过构造Lyapunov函数对系统进行分析,得到了方程系数的Khasminskii型条件。在此条件下证明了解的存在唯一性以及多项式的稳定性,并通过数值算例验证了该方法的有效性。

The polynomial stability of solutions for highly nonlinear hybrid stochastic delay differential equations (SDDEs) was discussed. The Lyapunov function was constructed to analyze the control system, and the Khasminskii condition of the equation coefficient was obtained. Based on these conditions, we proved the existence and uniqueness of solutions and the stability of polynomials. The feasibility of the method is verified by numerical examples.