The statistical dynamics of a spatial logistic model and the related kinetic equation
Abstract
There is studied an infinite system of point entities in which reproduce themselves and die, also due to competition. The system's states are probability measures on the space of configurations of entities. Their evolution is described by means of a BBGKY-type equation for the corresponding correlation (moment) functions. It is proved that: (a) these functions evolve on a bounded time interval and remain sub-Poissonian due to the competition; (b) in the Vlasov scaling limit they converge to the correlation functions of the time-dependent Poisson point field the density of which solves the kinetic equation obtained in the scaling limit from the equation for the correlation functions. A number of properties of the solutions of the kinetic equation are also established.
Keywords
Cite
@article{arxiv.1401.0557,
title = {The statistical dynamics of a spatial logistic model and the related kinetic equation},
author = {Dmitri Finkelshtein and Yuri Kondratiev and Yuri Kozitsky and Oleksandr Kutoviy},
journal= {arXiv preprint arXiv:1401.0557},
year = {2015}
}