Department of Mathematics and Interdisciplinary Program in Applied Mathematics, 617 N Santa Rita, University of Arizona, Tucson, AZ 85721, USA.
J Biol Dyn. 2012;6 Suppl 2:80-102. doi: 10.1080/17513758.2012.716085. Epub 2012 Aug 31.
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.
在本文中，我们考虑了用于研究具有单生活史的年龄结构种群动力学的非线性 Leslie 模型。我们建立了正平衡点的稳定性和不稳定性准则，这些平衡点从灭绝平衡点 R(0)=1 处分支出。当分支向右（向前或超临界）时，准则由涉及（低密度）类间和类内竞争强度的不等式组成。大致来说，如果类间竞争比类内竞争弱（强），则稳定性（不稳定性）发生。当分支向左（向后或亚临界）时，分支出的平衡点是不稳定的。我们还给出了确定正锥边界是吸引子还是排斥子的准则。这些一般准则有助于研究在低维单生活史 Leslie 模型中已知发生的动态二分法，即在平衡和年龄组同步振荡之间。
