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Survival analysis of stochastic competitive models in a polluted environment and stochastic competitive exclusion principle. (English) Zbl 1225.92059
Summary: 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.
60H10Stochastic ordinary differential equations
60H30Applications of stochastic analysis
65C20Models (numerical methods)
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