Evolution of infinite populations of immigrants: Micro- and mesoscopic description

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:477

Article

Kozitsky, Yuri¹ 

[1] Uniwersytet Marii Curie Sklodowskiej, Inst Matemat, PL-20031 Lublin, Poland

关键词: Complex system;    Infinite population;    Diversity;    Population dynamics;    Stochastic semigroup;    Kinetic equation;   

DOI  :  10.1016/j.jmaa.2019.04.033

来源: Elsevier

【 摘 要 】

A model is proposed of an infinite population of entities immigrating to a noncompact habitat, in which the newcomers are repelled by the already existing population. The evolution of such a population is described at micro- and mesoscopic levels. The microscopic states are probability measures on the corresponding configuration space. States of populations without interactions are Poisson measures, fully characterized by their densities. The evolution of micro-states is Markovian and obtained from the Kolmogorov equation with the use of correlation functions. The mesoscopic description is made by a kinetic equation for the densities. We show that the micro-states are approximated by the Poissonian states characterized by the densities obtained from the kinetic equation. Both micro-and mesoscopic descriptions are performed and their interrelations are analyzed, that includes also discussing the problem of the appearance of a spatial diversity in such populations. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free