On the Lotka-Volterra competition system with Allee effects

Sophia R.J. Jang

doi:10.1007/s40314-013-0022-x

On the Lotka-Volterra competition system with Allee effects

Sophia R.J. Jang

Mathematics and Statistics

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

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 language	English
Pages (from-to)	179-189
Number of pages	11
Journal	Computational and Applied Mathematics
Volume	32
Issue number	1
DOIs	https://doi.org/10.1007/s40314-013-0022-x
State	Published - Apr 2013

Keywords

Allee effects
Global stable manifolds
Monotone dynamical systems

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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.",

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AB - 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.

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On the Lotka-Volterra competition system with Allee effects

Abstract

Keywords

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