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Permanent URL to this publication: http://dx.doi.org/10.5167/uzh-21673

Barbour, A D; Pugliese, A (2005). Asymptotic behavior of a metapopulation model. Annals of Applied Probability, 15(2):1306-1338.

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Abstract

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.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
DDC:510 Mathematics
Uncontrolled Keywords:Metapopulation process; threshold theorem; stochastic comparison; structured population model
Language:English
Date:2005
Deposited On:03 Feb 2010 07:26
Last Modified:27 Nov 2013 19:08
Publisher:Institute of Mathematical Statistics
ISSN:1050-5164
Publisher DOI:10.1214/105051605000000070

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