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)

DOI: https://dx.doi.org/10.4310/CMS.2012.v10.n3.a12

Authors

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

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

Abstract

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.

Keywords

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

2010 Mathematics Subject Classification

60H10, 60H30, 92D25

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Published 9 April 2012