A bifurcation analysis of stage-structured density dependent integrodifference equations

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:388

Article

Robertson, Suzanne L.¹  Cushing, J. M.^1,2 

[1] Univ Arizona, Interdisciplinary Program Appl Math, Tucson, AZ 85721 USA

[2] Univ Arizona, Dept Math, Tucson, AZ 85721 USA

关键词: Bifurcation;    Net reproductive number;    Density dependent integrodifference equations;    Structured population dynamics;   

DOI  :  10.1016/j.jmaa.2011.09.064

来源: Elsevier

【 摘 要 】

There 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. (C) 2011 Elsevier Inc. All rights reserved.

【 授权许可】

Free