Extinction and quasi-stationarity in the Verhulst logistic model.

@article{Nsell2001ExtinctionAQ,
  title={Extinction and quasi-stationarity in the Verhulst logistic model.},
  author={Ingemar N{\aa}sell},
  journal={Journal of theoretical biology},
  year={2001},
  volume={211 1},
  pages={
          11-27
        }
}
  • I. Nåsell
  • Published 7 July 2001
  • Environmental Science
  • Journal of theoretical biology
We formulate and analyse a stochastic version of the Verhulst deterministic model for density-dependent growth of a single population. Three parameter regions with qualitatively different behaviours are identified. Explicit approximations of the quasi-stationary distribution and of the expected time to extinction are presented in each of these regions. The quasi-stationary distribution is approximately normal, and the time to extinction is long, in one of these regions. Another region has a… 
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