文章基本信息

标题：Stable bifurcations in semelparous Leslie models
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作者：J. M. Cushing ; Shandelle M. Henson
期刊名称：Journal of Biological Dynamics
印刷版ISSN：1751-3758
电子版ISSN：1751-3766
出版年度：2012
卷号：6
期号：sup2
页码：80-102
DOI：10.1080/17513758.2012.716085
出版社：Taylor & Francis
摘要：Formulae display: ? Mathematical formulae have been encoded as MathML and are displayed in this HTML version using MathJax in order to improve their display. Uncheck the box to turn MathJax off. This feature requires Javascript. Click on a formula to zoom. 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 R 0 =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.
关键词：nonlinear age-structured population dynamics; Leslie matrix; semelparity; bifurcation; equilibrium; synchronous cycles; stability