期刊
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
卷 381, 期 1, 页码 441-453出版社
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jmaa.2011.02.037
关键词
Stochastic differential equation; Density dependence; Beddington-DeAngelis functional response; Stationary distribution; Ergodicity; Extinction
资金
- NSFC of China [10971021]
- Ministry of Education of China [109051]
- Ph.D. Programs Foundation of Ministry of China [200918]
- NENU [09SSXT117]
In this paper, we discuss a stochastic density dependent predator-prey system with Beddington-DeAngelis functional response. First, we show that this system has a unique positive solution as this is essential in any population dynamics model. Then, we investigate the asymptotic behavior of this system. When the white noise is small, the stochastic system imitates the corresponding deterministic system. Either there is a stationary distribution, or the predator population will die out. While if The white noise is large, besides the extinction of the predator population, both species in the system may also die out, which does not happen in the deterministic system. Finally, simulations are carried out to conform to our results. (C) 2011 Elsevier Inc. All rights reserved.
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