Acta Biotheoretica

, Volume 62, Issue 3, pp 285–303

Reduction of Nonautonomous Population Dynamics Models with Two Time Scales

Regular Article

DOI: 10.1007/s10441-014-9221-0

Cite this article as:
Marvá, M. & Bravo de la Parra, R. Acta Biotheor (2014) 62: 285. doi:10.1007/s10441-014-9221-0

Abstract

The purpose of this work is reviewing some reduction results to deal with systems of nonautonomous ordinary differential equations with two time scales. They could be included among the so-called approximate aggregation methods. The existence of different time scales in a system, together with some long-term features, are used to build up a simpler system governed by a lesser number of state variables. The asymptotic behavior of the latter system is then used to describe the asymptotic behaviour of the former one. The reduction results are stated in two particular but important cases: periodic systems and asymptotically autonomous systems. The reduction results are illustrated with the help of simple spatial SIS epidemic models including either periodic or asymptotically autonomous terms.

Keywords

Slow–fast dynamics Singular perturbations Periodic systems Asymptotically autonomous systems Epidemic models 

Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.Department of Physics and MathematicsUniversity of Alcalá Campus UniversitarioAlcalá de HenaresSpain