Qualitative analysis of solutions to Lienard stochastic differential equation with multiple delays

Abstract

This study focuses on providing criteria for stochastic stability of the zero solution and uniform boundedness of solutions to a class of nonlinear Lienard stochastic differential equations with multiple bounded delays. A Lyapunov – Krasovskii functional is constructed and employed as a tool to prove our results. By our results, many stability and boundedness theorems of second order are improved on and are also generalized. The credibility of our results is demonstrated by two numerical examples included.