Stability analysis of a stochastic logistic model with infinite delay

This report is concerned with a stochastic logistic equation with infinite delay. We establish the sufficient conditions for global asymptotical stability of the zero solution and the positive equilibrium. Some classical results are improved and extended. Several numerical simulations are introduced to illustrate the main results.

► Stochastic Logistic model with infinite delay is proposed.
► Sufficient conditions for global stability of each equilibrium are established.
► Stochastic model will also be globally stable if the noise is not large.
► Numerical simulations are introduced to illustrate the results.