Bulletin of Mathematical Biology

, Volume 73, Issue 9, pp 1969–2012

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

Original Article

DOI: 10.1007/s11538-010-9569-5

Cite this article as:
Liu, M., Wang, K. & Wu, Q. Bull Math Biol (2011) 73: 1969. doi:10.1007/s11538-010-9569-5


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.


Competitive modelPolluted environmentStochastic disturbanceStochastic competitive exclusion principle

Copyright information

© Society for Mathematical Biology 2010

Authors and Affiliations

  1. 1.Department of MathematicsHarbin Institute of TechnologyWeihaiP.R. China
  2. 2.School of Mathematics and StatisticsNortheast Normal UniversityChangchunP.R. China