An extended discrete Ricker population model with Allee effects

Jia Li, Baojun Song, Xiaohong Wang

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Abstract

Based on the classical discrete Ricker population model, we incorporate Allee effects by assuming rectangular hyperbola, or Holling-II type functional form, for the birth or growth function and formulate an extended Ricker model. We explore the dynamics features of the extended Ricker model. We obtain domains of attraction for the trivial fixed point. We determine conditions for the existence and stability of positive fixed points and find regions where there exist no positive fixed points, two positive fixed points one of which is stable and two positive fixed points both of which are unstable. We demonstrate that the model exhibits period-doubling bifurcations and investigate the existence and stability of the cycles. We also confirm that Allee effects have stabilization effects, by different measures, through numerical simulations.

Original languageEnglish
Pages (from-to)309-321
Number of pages13
JournalJournal of Difference Equations and Applications
Volume13
Issue number4
DOIs
StatePublished - 1 Apr 2007

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Keywords

  • Allee effect
  • Period-doubling bifurcation
  • Ricker population model
  • Stabilization

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