Document Type

Article

Publication Date

9-1-2012

Keywords

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

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. © 2012 Copyright J.M. Cushing.

Journal Title

Journal of Biological Dynamics

Volume

6

Issue

SUPPL.2

First Page

80

Last Page

102

DOI

https://doi.org/10.1080/17513758.2012.716085

First Department

Mathematics

Acknowledgements

Retrieved February 3, 2010 from https://www.tandfonline.com/doi/full/10.1080/17513758.2012.716085

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