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Abstract and Applied Analysis
Volume 2012, Article ID 241702, 26 pages
Research Article

Stochastic Delay Logistic Model under Regime Switching

School of Mathematical Science, Anhui University, Hefei, Anhui 230039, China

Received 2 April 2012; Accepted 14 June 2012

Academic Editor: Elena Braverman

Copyright © 2012 Zheng Wu et al. 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.


This paper is concerned with a delay logistical model under regime switching diffusion in random environment. By using generalized Itô formula, Gronwall's inequality, and Young's inequality, some sufficient conditions for existence of global positive solutions and stochastically ultimate boundedness are obtained, respectively. Also, the relationships between the stochastic permanence and extinction as well as asymptotic estimations of solutions are investigated by virtue of -function technique, -matrix method, and Chebyshev's inequality. Finally, an example is given to illustrate the main results.