An extended discrete Ricker population model with Allee effects

Jia Li, Baojun Song, Xiaohong Wang

Research output: Contribution to journalArticleResearchpeer-review

22 Citations (Scopus)

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

Fingerprint

Allee Effect
Population Model
Discrete Model
Fixed point
Rectangular hyperbola
Growth Function
Period-doubling Bifurcation
Domain of Attraction
Stabilization
Trivial
Unstable
Model
Computer simulation
Cycle
Numerical Simulation
Demonstrate

Keywords

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

Cite this

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An extended discrete Ricker population model with Allee effects. / Li, Jia; Song, Baojun; Wang, Xiaohong.

In: Journal of Difference Equations and Applications, Vol. 13, No. 4, 01.04.2007, p. 309-321.

Research output: Contribution to journalArticleResearchpeer-review

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N2 - 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.

AB - 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.

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