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Asymptotic behavior of a metapopulation model


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

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.

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
Dewey Decimal Classification: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:05 Apr 2016 13:24
Publisher:Institute of Mathematical Statistics
ISSN:1050-5164
Publisher DOI:https://doi.org/10.1214/105051605000000070

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