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Aggregation of Variables and Applications to Population Dynamics

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Structured Population Models in Biology and Epidemiology

Part of the book series: Lecture Notes in Mathematics ((LNMBIOS,volume 1936))

Ecological modelers produce models with more and more details, leading to dynamical systems involving lots of variables. This chapter presents a set of methods which aim to extract from these complex models some submodels containing the same information but which are more tractable from the mathematical point of view. This “aggregation” of variables is based on time scales separation methods. The first part of the chapter is devoted to the presentation of mathematical aggregation methods for ODE’s, discrete models, PDE’s and DDE’s. The second part presents several applications in population and community dynamics.

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Authors and Affiliations

  1. IRD UR Géodes, Centre IRD de l’Ile de France, 32, Av. Henri Varagnat, 93143, Bondy cedex, France

    P. Auger, R. Bravo de la Parra & T. Nguyen-Huu

  2. Departamento de Matemáticas, Universidad de Alcalá, 28871, Alcalá de Henares, Madrid, Spain

    R. Bravo de la Parra

  3. Laboratoire de Microbiologie, Géochimie et d’Ecologie Marines, UMR 6117, Centre d’Océanologie de Marseille (OSU), Université de la Méditerranée, Case 901, Campus de Luminy, 13288, Marseille Cedex 9, France

    J. -C. Poggiale & T. Nguyen-Huu

  4. Departamento de Matemáticas, E.T.S.I. Industriales, U.P.M., c/ José Gutiérrez Abascal, 2, 28006, Madrid, Spain

    E. Sánchez

  5. IXXI, ENS Lyon, 46 allée d’Italie, 69364, Lyon cedex 07, France

    P. Auger & T. Nguyen-Huu

Authors
  1. P. Auger
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  2. R. Bravo de la Parra
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  3. J. -C. Poggiale
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  4. E. Sánchez
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  5. T. Nguyen-Huu
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Editor information

Editors and Affiliations

  1. University of Le Havre, 25 rue philippe Lebon, 76058, Le Havre, France

    Pierre Magal

  2. Department of Mathematics, University of Miami, Coral Gables, FL, 33124-4250, USA

    Shigui Ruan

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Auger, P., de la Parra, R.B., Poggiale, J.C., Sánchez, E., Nguyen-Huu, T. (2008). Aggregation of Variables and Applications to Population Dynamics. In: Magal, P., Ruan, S. (eds) Structured Population Models in Biology and Epidemiology. Lecture Notes in Mathematics, vol 1936. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-78273-5_5

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