A bifurcation analysis of stage-structured density dependent integrodifference equations

Suzanne L. Robertson, Jim M Cushing

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

There is evidence for density dependent dispersal in many stage-structured species, including flour beetles of the genus Tribolium. We develop a bifurcation theory approach to the existence and stability of (non-extinction) equilibria for a general class of structured integrodifference equation models on finite spatial domains with density dependent kernels, allowing for non-dispersing stages as well as partial dispersal. We show that a continuum of such equilibria bifurcates from the extinction equilibrium when it loses stability as the net reproductive number n increases through 1. Furthermore, the stability of the non-extinction equilibria is determined by the direction of the bifurcation. We provide an example to illustrate the theory.

Original languageEnglish (US)
Pages (from-to)490-499
Number of pages10
JournalJournal of Mathematical Analysis and Applications
Volume388
Issue number1
DOIs
StatePublished - Apr 1 2012

Fingerprint

Integrodifference Equations
Stage-structured
Bifurcation Analysis
Dependent
Reproductive number
Bifurcation Theory
Extinction
Genus
Continuum
Bifurcation
kernel
Partial

Keywords

  • Bifurcation
  • Density dependent integrodifference equations
  • Net reproductive number
  • Structured population dynamics

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

Cite this

A bifurcation analysis of stage-structured density dependent integrodifference equations. / Robertson, Suzanne L.; Cushing, Jim M.

In: Journal of Mathematical Analysis and Applications, Vol. 388, No. 1, 01.04.2012, p. 490-499.

Research output: Contribution to journalArticle

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