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).

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Zeitschriftenaufsatz | Veröffentlicht | Englisch
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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.
Erscheinungsjahr
Zeitschriftentitel
Mathematical Models and Methods in Applied Sciences
Band
25
Ausgabe
2
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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).
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). 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.
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).
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.
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, (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).