Discrete May-Leonard Competition Models I

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

Research output: Contribution to journalArticlepeer-review

25 Scopus citations


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 languageEnglish
Pages (from-to)77-98
Number of pages22
JournalJournal of Difference Equations and Applications
Issue number1
StatePublished - Jan 2004


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


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