Discrete May-Leonard Competition Models I

Lih Ing W. Roeger; Linda J.S. Allen

doi:10.1080/10236190310001603662

Discrete May-Leonard Competition Models I

Lih Ing W. Roeger, Linda J.S. Allen

Mathematics and Statistics

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

25 Scopus citations

Abstract

The local dynamics of two discrete-time models applicable to three competing plant species are shown to have properties similar to the May-Leonard (M-L) differential equation model. The dynamics of the two discrete models are shown to be similar. However, they are not dynamically consistent with the continuous M-L model. Unlike the continuous M-L model, the Hopf bifurcations of the discrete M-L models are not degenerate. The continuous M-L model is the limiting case of the discrete models.

Original language	English
Pages (from-to)	77-98
Number of pages	22
Journal	Journal of Difference Equations and Applications
Volume	10
Issue number	1
DOIs	https://doi.org/10.1080/10236190310001603662
State	Published - Jan 2004

Keywords

Competition
Difference equations
Hopf bifurcation
Lotka-Volterra
May-Leonard systems

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title = "Discrete May-Leonard Competition Models I",

abstract = "The local dynamics of two discrete-time models applicable to three competing plant species are shown to have properties similar to the May-Leonard (M-L) differential equation model. The dynamics of the two discrete models are shown to be similar. However, they are not dynamically consistent with the continuous M-L model. Unlike the continuous M-L model, the Hopf bifurcations of the discrete M-L models are not degenerate. The continuous M-L model is the limiting case of the discrete models.",

keywords = "Competition, Difference equations, Hopf bifurcation, Lotka-Volterra, May-Leonard systems",

author = "Roeger, {Lih Ing W.} and Allen, {Linda J.S.}",

note = "Funding Information: We thank Jack Hale for pointing out some Hopf bifurcation results in 3-dimensional systems. We thank the referees for their helpful comments and suggestions. The research of the second author was partially supported by National Science Foundation Grant, DMS-0201105.",

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AB - The local dynamics of two discrete-time models applicable to three competing plant species are shown to have properties similar to the May-Leonard (M-L) differential equation model. The dynamics of the two discrete models are shown to be similar. However, they are not dynamically consistent with the continuous M-L model. Unlike the continuous M-L model, the Hopf bifurcations of the discrete M-L models are not degenerate. The continuous M-L model is the limiting case of the discrete models.

KW - Competition

KW - Difference equations

KW - Hopf bifurcation

KW - Lotka-Volterra

KW - May-Leonard systems

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JO - Journal of Difference Equations and Applications

JF - Journal of Difference Equations and Applications

IS - 1

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Discrete May-Leonard Competition Models I

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Keywords

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