bifurcation, equilibrium, Leslie matrix, nonlinear age-structured population dynamics, semelparity, stability, synchronous cycles
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 of Biological Dynamics
Cushing, J. M. and Henson, Shandelle M., "Stable Bifurcations in Semelparous Leslie Models" (2012). Faculty Publications. 1678.
Retrieved February 3, 2010 from https://www.tandfonline.com/doi/full/10.1080/17513758.2012.716085