Asymptotic behavior of a metapopulation model
Copyright policy )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.
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)
- University of Trento Italy
- University of Zurich Switzerland
structured population model, 47J35, Nonlinear differential equations in abstract spaces, 34G20, Stability problems for infinite-dimensional dissipative dynamical systems, 60J27, 510 Mathematics, FOS: Mathematics, 1804 Statistics, Probability and Uncertainty, 2613 Statistics and Probability, Nonlinear evolution equations, Metapopulation process, metapopulation process, Ecology, threshold theorem, Probability (math.PR), 10123 Institute of Mathematics, Population dynamics (general), stochastic comparison, 37L15, 92D40, 37L15, 92D40 (Primary) 34G20, 47J35, 60J27. (Secondary), Mathematics - Probability, Continuous-time Markov processes on discrete state spaces
structured population model, 47J35, Nonlinear differential equations in abstract spaces, 34G20, Stability problems for infinite-dimensional dissipative dynamical systems, 60J27, 510 Mathematics, FOS: Mathematics, 1804 Statistics, Probability and Uncertainty, 2613 Statistics and Probability, Nonlinear evolution equations, Metapopulation process, metapopulation process, Ecology, threshold theorem, Probability (math.PR), 10123 Institute of Mathematics, Population dynamics (general), stochastic comparison, 37L15, 92D40, 37L15, 92D40 (Primary) 34G20, 47J35, 60J27. (Secondary), Mathematics - Probability, Continuous-time Markov processes on discrete state spaces
citations This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).20 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Average influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Top 10% impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Top 10%
Citations provided by BIP!Popularity provided by BIP!