Abstract and Applied Analysis
- Abstr. Appl. Anal.
- Volume 2012, Special Issue (2012), Article ID 241702, 26 pages.
Stochastic Delay Logistic Model under Regime Switching
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.
Abstr. Appl. Anal., Volume 2012, Special Issue (2012), Article ID 241702, 26 pages.
First available in Project Euclid: 1 April 2013
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Wu, Zheng; Huang, Hao; Wang, Lianglong. Stochastic Delay Logistic Model under Regime Switching. Abstr. Appl. Anal. 2012, Special Issue (2012), Article ID 241702, 26 pages. doi:10.1155/2012/241702. https://projecteuclid.org/euclid.aaa/1364846439