Asymptotic behavior of a metapopulation model

• 成果类型: Article
• 署名作者: Barbour, AD; Pugliese, A
• 署名单位: University of Zurich; University of Trento
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/105051605000000070
• 发表日期: 2005
• 页码: 1306-1338
• 关键词: persistence; extinction; fitness

摘要

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.