Fixed points and stability of A class of Stochastic dynamical system driven by Brownian motion

Abstract

In real life, many models and systems are affected by random phenomena. For this reason, experts and scholars propose to describe these stochastic processes with Brownian motion respectively. In this paper we consider a kind of stochastic Vollterra dynamical systems of nonconvolution type and give some new conditions to ensure that the zero solution is asymptotically stable in mean square by means of fixed point method. The theorems of asymptotically stability in mean square with a necessary conditions are proved. Some results of related papers are improved.