A note on nonautonomous logistic equation with random perturbation

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Abstract

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 ∫0T[a(s) - α2(s)]ds > 0. © 2004 Elsevier Inc. All rights reserved.

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Jiang, D., & Shi, N. (2005). A note on nonautonomous logistic equation with random perturbation. Journal of Mathematical Analysis and Applications, 303(1), 164–172. https://doi.org/10.1016/j.jmaa.2004.08.027

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