Asymptotic behavior of a metapopulation model
نویسنده
چکیده
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. The Annals of Applied Probability 2005, Vol. 15, No. 2, 1306–1338 DOI 10.1214/105051605000000070 © Institute of Mathematical Statistics, 2005 ASYMPTOTIC BEHAVIOR OF A METAPOPULATION MODEL BY A. D. BARBOUR1 AND A. PUGLIESE2 Universität Zürich and Universitá di Trento 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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