Asymptotic behavior of a metapopulation model

Details Asymptotic behavior of a metapopulation model Asymptotic behavior of a metapopulation model

2005-05-12

arxiv.org/abs/math/0505240v1

Annals of Applied Probability 2005, Vol. 15, No. 2, 1306-1338

Mathematics

Probability

Published at http://dx.doi.org/10.1214/105051605000000070 in the Annals of Applied Probability (http://www.imstat.org/aap/) by

Scientific paper

10.1214/105051605000000070

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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