Stability analysis of a stochastic logistic model

We provide asymptotic analysis of equilibrium states of a stochastic logistic population model for a single species. The model is based on a stochastic differential equation with a nonlinear diffusion term. Both Itô and Stratonovič interpretations are considered. We obtain sufficient conditions for stability by means of the Liapunov second method. We also present results of a numerical simulation for the considered stochastic logistic model.