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

Finkelshtein D, Kondratiev Y, Kozitsky Y, Kutoviy O (2015)
Mathematical Models and Methods in Applied Sciences 25(2): 343-370.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Autor*in
Finkelshtein, Dmitri; Kondratiev, YuriUniBi; Kozitsky, Yuri; Kutoviy, Oleksandr
Abstract / Bemerkung
In this paper, we study an infinite system of point entities in 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.
Stichworte
Individual-based model; birth-and-death process; Ovcyannikov's method; random point field
Erscheinungsjahr
2015
Zeitschriftentitel
Mathematical Models and Methods in Applied Sciences
Band
25
Ausgabe
2
Seite(n)
343-370
ISSN
0218-2025
Page URI
https://pub.uni-bielefeld.de/record/2762773

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Finkelshtein D, Kondratiev Y, Kozitsky Y, Kutoviy O. The statistical dynamics of a spatial logistic model and the related kinetic equation. Mathematical Models and Methods in Applied Sciences. 2015;25(2):343-370.
Finkelshtein, D., Kondratiev, Y., Kozitsky, Y., & Kutoviy, O. (2015). The statistical dynamics of a spatial logistic model and the related kinetic equation. Mathematical Models and Methods in Applied Sciences, 25(2), 343-370. doi:10.1142/S0218202515500128
Finkelshtein, D., Kondratiev, Y., Kozitsky, Y., and Kutoviy, O. (2015). The statistical dynamics of a spatial logistic model and the related kinetic equation. Mathematical Models and Methods in Applied Sciences 25, 343-370.
Finkelshtein, D., et al., 2015. The statistical dynamics of a spatial logistic model and the related kinetic equation. Mathematical Models and Methods in Applied Sciences, 25(2), p 343-370.
D. Finkelshtein, et al., “The statistical dynamics of a spatial logistic model and the related kinetic equation”, Mathematical Models and Methods in Applied Sciences, vol. 25, 2015, pp. 343-370.
Finkelshtein, D., Kondratiev, Y., Kozitsky, Y., Kutoviy, O.: The statistical dynamics of a spatial logistic model and the related kinetic equation. Mathematical Models and Methods in Applied Sciences. 25, 343-370 (2015).
Finkelshtein, Dmitri, Kondratiev, Yuri, Kozitsky, Yuri, and Kutoviy, Oleksandr. “The statistical dynamics of a spatial logistic model and the related kinetic equation”. Mathematical Models and Methods in Applied Sciences 25.2 (2015): 343-370.