On the Lotka-Volterra competition system with Allee effects

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Abstract

We study asymptotic dynamics of the classical Lotka-Volterra competition model when both competing populations are subject to Allee effects. The resulting system can have up to four interior steady states. In such case, it is proved that both competing populations may either go extinct, coexist, or one population drives the other population to extinction depending on initial conditions.

Original languageEnglish
Pages (from-to)179-189
Number of pages11
JournalComputational and Applied Mathematics
Volume32
Issue number1
DOIs
StatePublished - Apr 2013

Keywords

  • Allee effects
  • Global stable manifolds
  • Monotone dynamical systems

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