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Mathematical Problems in Engineering
Volume 2014, Article ID 495275, 8 pages
http://dx.doi.org/10.1155/2014/495275
Research Article

Permanence and Extinction of a Stochastic Delay Logistic Model with Jumps

1Department of Mathematics, Harbin Institute of Technology (Weihai), Weihai 264209, China
2School of Science, Qingdao Technological University, Qingdao 266520, China

Received 3 October 2013; Revised 10 December 2013; Accepted 25 December 2013; Published 16 February 2014

Academic Editor: Asier Ibeas

Copyright © 2014 Chun Lu and Xiaohua Ding. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

This paper is concerned with a stochastic delay logistic model with jumps. Sufficient and necessary conditions for extinction are obtained as well as stochastic permanence. Numerical simulations are introduced to support the theoretical analysis results. The results show that the jump process can affect the properties of the population model significantly, which conforms to biological significance.