We study the behaviour of an infinite system of ordinary differential equations modelling the dynamics of a meta-population, 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 meta-population, 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

Asymptotic behavior of a metapopulation model / A., Barbour; Pugliese, Andrea. - In: THE ANNALS OF APPLIED PROBABILITY. - ISSN 1050-5164. - STAMPA. - 15:(2005), pp. 1306-1338.

Asymptotic behavior of a metapopulation model

Pugliese, Andrea
2005

Abstract

We study the behaviour of an infinite system of ordinary differential equations modelling the dynamics of a meta-population, 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 meta-population, 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
A., Barbour; Pugliese, Andrea
Asymptotic behavior of a metapopulation model / A., Barbour; Pugliese, Andrea. - In: THE ANNALS OF APPLIED PROBABILITY. - ISSN 1050-5164. - STAMPA. - 15:(2005), pp. 1306-1338.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11572/72336
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