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Erschienen in: Automatic Control and Computer Sciences 7/2019

01.12.2019

Dynamics of Population Distribution by Patches

verfasst von: A. N. Kirillov, I. V. Danilova

Erschienen in: Automatic Control and Computer Sciences | Ausgabe 7/2019

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Abstract

This paper considers the patch selection by a population without having full information about the utility of the patch, i.e., the amount of its energy resources. This problem is related to the optimal foraging theory. According to U. Dieckmann’s suggestion, the population distribution by patches should be modeled according to the utility function that takes into account the amount of resources per patch, the population–patch distance, and the extent to which the population is aware of the amount of resources in the patch. In this case, the population distribution by patches is described using the Boltzmann distribution. Dieckmann considers a static problem without taking into account the change in the position of the population over time. In this paper, we suggest a dynamic system that describes the population distribution by patches, which depends on the utility of patches that changes over time as a result of variations in the population–patch distance. That said, the Boltzmann distribution is a particular solution of the derived system of ordinary differential equations. The Lyapunov stability condition for the Boltzmann distribution is derived. The patch utility functions dependent on the distance to and the population’s awareness of the patch are introduced. As a result, in the 2D case the R2 space in divided in preferential utility domains. This partition generalizes G.F. Voronoy’s diagram.
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Metadaten
Titel
Dynamics of Population Distribution by Patches
verfasst von
A. N. Kirillov
I. V. Danilova
Publikationsdatum
01.12.2019
Verlag
Pleiades Publishing
Erschienen in
Automatic Control and Computer Sciences / Ausgabe 7/2019
Print ISSN: 0146-4116
Elektronische ISSN: 1558-108X
DOI
https://doi.org/10.3103/S0146411619070095

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