355 research outputs found
Asymptotic behavior of a metapopulation model
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.Comment: Published at http://dx.doi.org/10.1214/105051605000000070 in the
Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute
of Mathematical Statistics (http://www.imstat.org
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