We study the behavior of an infinite system of ordinary differential equations modeling the dynamics of a metapopulation, a set of (discrete) populations subject to local catastrophes and connected via migration under a mean field rule; the local population dynamics follow a generalized logistic law. We find a threshold below which all the solutions tend to total extinction of the metapopulation, which is then the only equilibrium; above the threshold, there exists a unique equilibrium with positive population, which, under an additional assumption, is globally attractive. The proofs employ tools from the theories of Markov processes and of dynamical systems.
Publié le : 2005-05-14
Classification:
Metapopulation process,
threshold theorem,
stochastic comparison,
structured population model,
37L15,
92D40,
34G20,
47J35,
60J27
@article{1115137976,
author = {Barbour, A. D. and Pugliese, A.},
title = {Asymptotic behavior of a metapopulation model},
journal = {Ann. Appl. Probab.},
volume = {15},
number = {1A},
year = {2005},
pages = { 1306-1338},
language = {en},
url = {http://dml.mathdoc.fr/item/1115137976}
}
Barbour, A. D.; Pugliese, A. Asymptotic behavior of a metapopulation model. Ann. Appl. Probab., Tome 15 (2005) no. 1A, pp. 1306-1338. http://gdmltest.u-ga.fr/item/1115137976/