TY - JOUR
T1 - A bifurcation analysis of stage-structured density dependent integrodifference equations
AU - Robertson, Suzanne L.
AU - Cushing, J. M.
N1 - Funding Information:
This work was done as part of S.L. Robertson’s PhD thesis, Spatial patterns in stage-structured populations with density dependent dispersal, Interdisciplinary Program in Applied Mathematics, University of Arizona, 2009 and was supported in part by National Science Foundation grant DMS-0414212.
PY - 2012/4/1
Y1 - 2012/4/1
N2 - 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.
AB - 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.
KW - Bifurcation
KW - Density dependent integrodifference equations
KW - Net reproductive number
KW - Structured population dynamics
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U2 - 10.1016/j.jmaa.2011.09.064
DO - 10.1016/j.jmaa.2011.09.064
M3 - Article
AN - SCOPUS:84455188938
SN - 0022-247X
VL - 388
SP - 490
EP - 499
JO - Journal of Mathematical Analysis and Applications
JF - Journal of Mathematical Analysis and Applications
IS - 1
ER -