A bifurcation analysis of stage-structured density dependent integrodifference equations |
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Authors: | Suzanne L Robertson JM Cushing |
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Institution: | 1. Interdisciplinary Program in Applied Mathematics, University of Arizona, Tucson, AZ 85721, USA;2. Department of Mathematics, University of Arizona, Tucson, AZ 85721, USA |
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Abstract: | 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. |
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