Communications in Mathematical Sciences

Volume 10 (2012)

Number 3

Persistence and extinction of a non-autonomous logistic model with random perturbations

Pages: 977 – 987

(Fast Communication)



Meng Liu (School of Mathematical Science, Huaiyin Normal University, Huaian, China)

Ke Wang (Department of Mathematics, Harbin Institute of Technology, Weihai, China)


This paper is concerned with the persistence and extinction of a randomized nonautonomous logistic system. Sufficient conditions for extinction, non-persistence in the mean, weak persistence and stochastic permanence are established. The critical value between weak persistence, and extinction is obtained. The behaviors of the system in every coefficient case are studied.


non-autonomous logistic model, random perturbations, persistence, extinction

2010 Mathematics Subject Classification

60H10, 60H30, 92D25

Full Text (PDF format)