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arXiv · 1401.0557

The statistical dynamics of a spatial logistic model and the related kinetic equation

Dmitri Finkelshtein·Yuri Kondratiev·Yuri Kozitsky·Oleksandr Kutoviy
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Abstract

There is studied an infinite system of point entities in $\mathbb{R}^d$ 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.

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Dmitri Finkelshtein, Yuri Kondratiev, Yuri Kozitsky, Oleksandr Kutoviy. 2014-12-04. The statistical dynamics of a spatial logistic model and the related kinetic equation. https://doi.org/10.1142/s0218202515500128

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