Reduction of Discrete Dynamical Systems with Applications to Dynamics Population Models

Bravo de la Parra, Rafael and Marvá, M. and Sánchez., E. and Sanz Lorenzo, Luis (2013). Reduction of Discrete Dynamical Systems with Applications to Dynamics Population Models. "Mathematical Modelling of Natural Phenomena", v. 8 (n. 6); pp. 107-129. ISSN 0973-5348. https://doi.org/10.1051/mmnp/20138608.

Description

Title: Reduction of Discrete Dynamical Systems with Applications to Dynamics Population Models
Author/s:
  • Bravo de la Parra, Rafael
  • Marvá, M.
  • Sánchez., E.
  • Sanz Lorenzo, Luis
Item Type: Article
Título de Revista/Publicación: Mathematical Modelling of Natural Phenomena
Date: 2013
Volume: 8
Subjects:
Freetext Keywords: discrete models, aggregation of variables, time scales, population dynamic
Faculty: E.T.S.I. Industriales (UPM)
Department: Matemática Aplicada
Creative Commons Licenses: Recognition - No derivative works - Non commercial

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Abstract

In this work we review the aggregation of variables method for discrete dynamical systems. These methods consist of describing the asymptotic behaviour of a complex system involving many coupled variables through the asymptotic behaviour of a reduced system formulated in terms of a few global variables. We consider population dynamics models including two processes acting at different time scales. Each process has associated a map describing its effect along its specific time unit. The discrete system encompassing both processes is expressed in the slow time scale composing the map associated to the slow one and the k-th iterate of the map associated to the fast one. In the linear case a result is stated showing the relationship between the corresponding asymptotic elements of both systems, initial and reduced. In the nonlinear case, the reduction result establishes the existence, stability and basins of attraction of steady states and periodic solutions of the original system with the help of the same elements of the corresponding reduced system. Several models looking over the main applications of the method to populations dynamics are collected to illustrate the general results.

Funding Projects

TypeCodeAcronymLeaderTitle
Government of SpainMTM2011-24321UnspecifiedUnspecifiedUnspecified
Government of SpainMTM2011-25238UnspecifiedUnspecifiedUnspecified

More information

Item ID: 49338
DC Identifier: http://oa.upm.es/49338/
OAI Identifier: oai:oa.upm.es:49338
DOI: 10.1051/mmnp/20138608
Official URL: https://www.mmnp-journal.org/articles/mmnp/abs/2013/06/mmnp201386p107/mmnp201386p107.html
Deposited by: Memoria Investigacion
Deposited on: 01 Feb 2018 16:21
Last Modified: 01 Feb 2018 16:21
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