A bifurcation analysis of stage-structured density dependent integrodifference equations

• DOI: 10.1016/j.jmaa.2011.09.064
• Publication Date: 2011-10-02T04:48:39Z
• Authors: Suzanne L. Robertson; J.M. Cushing
• Keywords: 0301 basic medicine; 03 medical and health sciences; Density dependent integrodifference equations; Structured population dynamics; Applied Mathematics; Bifurcation; Net reproductive number; Analysis

AbstractThere 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.