On the Lotka–Volterra competition system with Allee effects

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...

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Bibliographic Details
Published inComputational and Applied Mathematics Vol. 32; no. 1; pp. 179 - 189
Main Author Jang, Sophia R.-J.
Format Journal Article
LanguageEnglish
Published Basel SP Birkhäuser Verlag Basel 01.04.2013
Subjects
Applications of Mathematics
Computational Mathematics and Numerical Analysis
Mathematical Applications in Computer Science
Mathematical Applications in the Physical Sciences
Mathematics
Mathematics and Statistics
Allee effects
Global stable manifolds
92D25
92D40
Monotone dynamical systems
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Summary: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.
ISSN:0101-8205
1807-0302
DOI:10.1007/s40314-013-0022-x