Aggregation methods in dynamical systems and applications in population and community dynamics

Auger, Pierre and Bravo de la Parra, Rafael and Poggiale, Jean-Christophe and Sánchez Mañes, Eva María and Sanz Lorenzo, Luis (2008). Aggregation methods in dynamical systems and applications in population and community dynamics. "Physics of Life Reviews", v. 5 (n. 2); pp. 79-105. ISSN 1571-0645. https://doi.org/10.1016/j.plrev.2008.02.001.

Description

Title: Aggregation methods in dynamical systems and applications in population and community dynamics
Author/s:
  • Auger, Pierre
  • Bravo de la Parra, Rafael
  • Poggiale, Jean-Christophe
  • Sánchez Mañes, Eva María
  • Sanz Lorenzo, Luis
Item Type: Article
Título de Revista/Publicación: Physics of Life Reviews
Date: June 2008
ISSN: 1571-0645
Volume: 5
Subjects:
Freetext Keywords: Approximate aggregation of variables; population dynamics; time scales; dynamical systems
Faculty: E.T.S.I. Industriales (UPM)
Department: Matemática Aplicada a la Ingeniería Industrial
Creative Commons Licenses: Recognition - No derivative works - Non commercial

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Abstract

Approximate aggregation techniques allow one to transform a complex system involving many coupled variables into a simpler reduced model with a lesser number of global variables in such a way that the dynamics of the former can be approximated by that of the latter. In ecology, as a paradigmatic example, we are faced with modelling complex systems involving many variables corresponding to various interacting organization levels. This review is devoted to approximate aggregation methods that are based on the existence of different time scales, which is the case in many real systems as ecological ones where the different organization levels (individual, population, community and ecosystem) possess a different characteristic time scale. Two main goals of variables aggregation are dealt with in this work. The first one is to reduce the dimension of the mathematical model to be handled analytically and the second one is to understand how different organization levels interact and which properties of a given level emerge at other levels. The review is organized in three sections devoted to aggregation methods associated to different mathematical formalisms: ordinary differential equations, infinite-dimensional evolution equations and difference equations.

More information

Item ID: 2250
DC Identifier: http://oa.upm.es/2250/
OAI Identifier: oai:oa.upm.es:2250
DOI: 10.1016/j.plrev.2008.02.001
Official URL: http://www.elsevier.com/wps/find/journaldescription.cws_home/680835/description#description
Deposited by: Memoria Investigacion
Deposited on: 19 May 2010 10:56
Last Modified: 20 Apr 2016 11:59
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