Aggregation, Emergence and Immergence in Hierarchically Organized Systems

Auger, Pierre; Chiorino, Giovanna; Poggiale, Jean-Christophe

doi:10.1080/03081079908962070

Cited by 3 publications

(2 citation statements)

References 21 publications

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“…His proof may also be obtained by Fenichel's methods. Our reduction method is based on this approach, see Auger et al [9,11], and Auger and Poggiale [12][13][14][15]. Note that the Fenichel theorem has been extended to semi-groups on Banach spaces by Bates et al [19,20].…”

Section: Normally Hyperbolic Manifolds and Gsp Theorymentioning

confidence: 99%

Aggregation of Variables and Applications to Population Dynamics

Auger

Parra

Poggiale³

et al. 2008

Structured Population Models in Biology and Epidemiology

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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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Section: Normally Hyperbolic Manifolds and Gsp Theorymentioning

confidence: 99%

Aggregation of Variables and Applications to Population Dynamics

Auger

Parra

Poggiale³

et al. 2008

Structured Population Models in Biology and Epidemiology

View full text Add to dashboard Cite

show abstract

“…His proof mav also be obtained by Fenichel's methods. Our reduction method is based on this approach, Auger et al in 1999Auger and Poggiale in 1995 Note that the Fenichel theorem has been extended to semi-groups on Banach spaces by Bates et al in 1998 andin 2000 2.3…”

Section: Normally Hyperbolic Manifolds and Gsp Theorymentioning

confidence: 99%

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

Auger

Parra

Poggiale

et al. 2008

Physics of Life Reviews

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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.

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Financial Applications of Fractional Brownian Motion

2008

Lecture Notes in Mathematics

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Aggregation, Emergence and Immergence in Hierarchically Organized Systems

Cited by 3 publications

References 21 publications

Aggregation of Variables and Applications to Population Dynamics

Aggregation of Variables and Applications to Population Dynamics

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

Financial Applications of Fractional Brownian Motion

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