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[1/N(t )] has a unique positive T -periodic solution E[1/Np(t )] provided a(t), b(t ), and α(t) are continuous T -periodic functions, a(t) > 0, b(t ) > 0 and T 0 [a(s) − α2(s)]ds >0.  2004 Elsevier Inc. All rights reserved.