Reduction of Discrete Dynamical Systems with Applications to Dynamics Population Models

Bravo de la Parra, Rafael; Marvá, M.; Sánchez., E. y 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.

Descripción

Título: Reduction of Discrete Dynamical Systems with Applications to Dynamics Population Models
Autor/es:
  • Bravo de la Parra, Rafael
  • Marvá, M.
  • Sánchez., E.
  • Sanz Lorenzo, Luis
Tipo de Documento: Artículo
Título de Revista/Publicación: Mathematical Modelling of Natural Phenomena
Fecha: 2013
Volumen: 8
Materias:
Palabras Clave Informales: discrete models, aggregation of variables, time scales, population dynamic
Escuela: E.T.S.I. Industriales (UPM)
Departamento: Matemática Aplicada
Licencias Creative Commons: Reconocimiento - Sin obra derivada - No comercial

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Resumen

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.

Proyectos asociados

TipoCódigoAcrónimoResponsableTítulo
Gobierno de EspañaMTM2011-24321Sin especificarSin especificarSin especificar
Gobierno de EspañaMTM2011-25238Sin especificarSin especificarSin especificar

Más información

ID de Registro: 49338
Identificador DC: http://oa.upm.es/49338/
Identificador OAI: oai:oa.upm.es:49338
Identificador DOI: 10.1051/mmnp/20138608
URL Oficial: https://www.mmnp-journal.org/articles/mmnp/abs/2013/06/mmnp201386p107/mmnp201386p107.html
Depositado por: Memoria Investigacion
Depositado el: 01 Feb 2018 16:21
Ultima Modificación: 01 Feb 2018 16:21
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