期刊
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
卷 388, 期 1, 页码 490-499出版社
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jmaa.2011.09.064
关键词
Bifurcation; Net reproductive number; Density dependent integrodifference equations; Structured population dynamics
资金
- National Science Foundation [DMS-0414212]
- Direct For Mathematical & Physical Scien
- Division Of Mathematical Sciences [917435] Funding Source: National Science Foundation
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.
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