Stochastic evolution of a continuum particle system with dispersal and competition

Finkelshtein D, Kondratiev Y, Kozitsky Y, Kutoviy O (2013)
The European Physical Journal Special Topics 216(1): 107-116.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Autor*in
Finkelshtein, Dmitri; Kondratiev, YuriUniBi; Kozitsky, Yuri; Kutoviy, Oleksandr
Abstract / Bemerkung
A Markov evolution of a system of point particles in a"e (d) is described at micro- and mesoscopic levels. The particles reproduce themselves at distant points (dispersal) and die, independently and under the effect of each other (competition). The microscopic description is based on an infinite chain of equations for correlation functions, similar to the BBGKY hierarchy used in the Hamiltonian dynamics of continuum particle systems. The mesoscopic description is based on a Vlasov-type kinetic equation for the particle's density obtained from the mentioned chain via a scaling procedure. The main conclusion of the microscopic theory is that the competition can prevent the system from clustering, which makes its description in terms of densities reasonable. A possible homogenization of the solutions to the kinetic equation in the long-time limit is also discussed.
Erscheinungsjahr
2013
Zeitschriftentitel
The European Physical Journal Special Topics
Band
216
Ausgabe
1
Seite(n)
107-116
ISSN
1951-6355
Page URI
https://pub.uni-bielefeld.de/record/2560181

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Finkelshtein D, Kondratiev Y, Kozitsky Y, Kutoviy O. Stochastic evolution of a continuum particle system with dispersal and competition. The European Physical Journal Special Topics. 2013;216(1):107-116.
Finkelshtein, D., Kondratiev, Y., Kozitsky, Y., & Kutoviy, O. (2013). Stochastic evolution of a continuum particle system with dispersal and competition. The European Physical Journal Special Topics, 216(1), 107-116. doi:10.1140/epjst/e2013-01733-3
Finkelshtein, D., Kondratiev, Y., Kozitsky, Y., and Kutoviy, O. (2013). Stochastic evolution of a continuum particle system with dispersal and competition. The European Physical Journal Special Topics 216, 107-116.
Finkelshtein, D., et al., 2013. Stochastic evolution of a continuum particle system with dispersal and competition. The European Physical Journal Special Topics, 216(1), p 107-116.
D. Finkelshtein, et al., “Stochastic evolution of a continuum particle system with dispersal and competition”, The European Physical Journal Special Topics, vol. 216, 2013, pp. 107-116.
Finkelshtein, D., Kondratiev, Y., Kozitsky, Y., Kutoviy, O.: Stochastic evolution of a continuum particle system with dispersal and competition. The European Physical Journal Special Topics. 216, 107-116 (2013).
Finkelshtein, Dmitri, Kondratiev, Yuri, Kozitsky, Yuri, and Kutoviy, Oleksandr. “Stochastic evolution of a continuum particle system with dispersal and competition”. The European Physical Journal Special Topics 216.1 (2013): 107-116.

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