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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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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|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|
|Deposited On:||03 Feb 2010 07:26|
|Last Modified:||27 Nov 2013 19:08|
|Publisher:||Institute of Mathematical Statistics|
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