Journal
BULLETIN OF MATHEMATICAL BIOLOGY
Volume 77, Issue 7, Pages 1285-1326Publisher
SPRINGER
DOI: 10.1007/s11538-015-0086-4
Keywords
Stochastic competition model; Polluted environment; It(o)over-cap's formula; Survival analysis; Stationary distribution
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Funding
- National Natural Science Foundation of China [11271260]
- Shanghai Leading Academic Discipline Project [XTKX2012]
- Hujiang Foundation of China [B14005]
- Innovation Program of Shanghai Municipal Education Committee [13ZZ116]
- Natural Science Foundation of Ningxia [NZ13212]
- University Scientific Research Project in Ningxia [NGY2013108]
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In this paper, we develop and study a stochastic model for the competition of three species with a generalized dose-response function in a polluted environment. We first carry out the survival analysis and obtain sufficient conditions for the extinction, non-persistence, weak persistence in the mean, strong persistence in the mean and stochastic permanence. The threshold between weak persistence in the mean and extinction is established for each species. Then, using Hasminskii's methods and a Lyapunov function, we derive sufficient conditions for the existence of stationary distribution for each population. Numerical simulations are carried out to support our theoretical results, and some biological significance is presented.
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