Stable bifurcations in semelparous Leslie models

J. M. Cushing, Shandelle M. Henson

Research output: Contribution to journalArticle

17 Scopus citations

Abstract

In this paper, we consider nonlinear Leslie models for the dynamics of semelparous age-structured populations. We establish stability and instability criteria for positive equilibria that bifurcate from the extinction equilibrium at R0=1. When the bifurcation is to the right (forward or super-critical), the criteria consist of inequalities involving the (low-density) between-class and within-class competition intensities. Roughly speaking, stability (respectively, instability) occurs if between-class competition is weaker (respectively, stronger) than within-class competition. When the bifurcation is to the left (backward or sub-critical), the bifurcating equilibria are unstable. We also give criteria that determine whether the boundary of the positive cone is an attractor or a repeller. These general criteria contribute to the study of dynamic dichotomies, known to occur in lower dimensional semelparous Leslie models, between equilibration and age-cohort-synchronized oscillations.

Original languageEnglish (US)
Pages (from-to)80-102
Number of pages23
JournalJournal of biological dynamics
Volume6
Issue numberSUPPL.2
DOIs
StatePublished - Sep 1 2012

Keywords

  • Leslie matrix
  • bifurcation
  • equilibrium
  • nonlinear age-structured population dynamics
  • semelparity
  • stability
  • synchronous cycles

ASJC Scopus subject areas

  • Ecology, Evolution, Behavior and Systematics
  • Ecology

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