Asymptotic behavior of a stochastic microorganism flocculation model with time delay

Abstract

In this paper, we consider a microorganism flocculation model with stochastic perturbation and time delay. By constructing some suitable Lyapunov functions, the asymptotic behaviors of the solution of the stochastic model around the equilibria of the corresponding deterministic model are investigated. We find that the average in time of the second moment of the solutions of the stochastic system is bounded to a relatively small noise.