A note on nonautonomous logistic equation with random perturbation

This paper discusses a randomized nonautonomous logistic equation dN(t)=N(t)[(a(t)−b(t)N(t))dt+α(t)dB(t)], where B(t) is 1-dimensional standard Brownian motion. We show that E[1N(t)] has a unique positive T-periodic solution E[1Np(t)] provided a(t), b(t), and α(t) are continuous T-periodic functions, a(t)>0, b(t)>0 and ∫0T[a(s)−α2(s)]ds>0.