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Asymptotic behavior of a metapopulation model

A. D. Barbour·A. Pugliese
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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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BibTeXRIS

A. D. Barbour, A. Pugliese. 2005-05-12. Asymptotic behavior of a metapopulation model. https://doi.org/10.1214/105051605000000070

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