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Survival Analysis of Stochastic Competitive Models in a Polluted Environment and Stochastic Competitive Exclusion Principle

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Abstract

Stochastic competitive models with pollution and without pollution are proposed and studied. For the first system with pollution, sufficient criteria for extinction, nonpersistence in the mean, weak persistence in the mean, strong persistence in the mean, and stochastic permanence are established. The threshold between weak persistence in the mean and extinction for each population is obtained. It is found that stochastic disturbance is favorable for the survival of one species and is unfavorable for the survival of the other species. For the second system with pollution, sufficient conditions for extinction and weak persistence are obtained. For the model without pollution, a partial stochastic competitive exclusion principle is derived.

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Authors and Affiliations

  1. Department of Mathematics, Harbin Institute of Technology, Weihai, 264209, P.R. China

    Meng Liu, Ke Wang & Qiong Wu

  2. School of Mathematics and Statistics, Northeast Normal University, Changchun, 130024, P.R. China

    Ke Wang

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  1. Meng Liu
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  2. Ke Wang
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  3. Qiong Wu
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Correspondence to Meng Liu.

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Liu, M., Wang, K. & Wu, Q. Survival Analysis of Stochastic Competitive Models in a Polluted Environment and Stochastic Competitive Exclusion Principle. Bull Math Biol 73, 1969–2012 (2011). https://doi.org/10.1007/s11538-010-9569-5

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