Description Note Author(s) References

GPoM is a platform dedicated to the Global Modelling technique. Its aim is to obtain deterministic models of Ordinary Differential Equations from observational time series. It applies to single and to multiple time series. With single time series, it can be used: to detect low-dimnesional determinism and low-dimensional (deterministic) chaos. It can also be used to characterize the observed behavior, using the obtained models as a proxy of the original dynamics, as far as the model validation could be checked. With multiple time series, it can be used: to detect couplings between observed variables, to infer causal networks, and to reformulate the original equations of the observed system (retro-modelling). The present package focuses on models in Ordinary Differential Equations of polynomial form. The package was designed to model weakly predictable dynamical behaviors (such as chaotic behaviors). Of course, it can also apply to more of fully predictable behavior, either linear or nonlinear. Several vignettes are associated to the package which can be used as a tutorial, and it also provides an overlook of the diversity of applications and at the performances of the tools. Users are kindly asked to quote the corresponding references when using the package (see hereafter).

FOR USERS

This package was developped at Centre d'Etudes Spatiales de
la Biosphere (Cesbio, UMR 5126, UPS-CNRS-CNES-IRD,
http://www.cesbio.ups-tlse.fr).
An important part of the developments were funded by
the French program Les Enveloppes Fluides et l'Environnement
(LEFE, MANU, projets GloMo, SpatioGloMo and MoMu).
The French program DÃ©fi InFiNiTi (CNRS) and PNTS
are also acknowledged (projects Crops'IChaos and Musc & SlowFast).

If you apply this package to single time series, please quote [6]. If you apply it to multivariate time series, please quote [10]. If you apply it to infer couplings among time series, please quote [8]. If you apply it to classification, please quote [11].

HISTORICAL BACKGROUND

The global modelling technique was initiated during
the early 1990s [1-3]. It takes its background from
the Theory of Nonlinear Dynamical Systems.
Earlier investigations can also be found in the fields
of Electrical Engineering and Statistics but these
mainly focused on linear problems [4].
The approach became applicable to the analysis of real world
environmental behaviours by the end of the 2000s [5-7].
Recent works have shown that the approach could be applied to
numerous other dynamical behaviors [8-10].
Global modelling aims to obtain deterministic models
directly from observed time series.

Sylvain Mangiarotti, Flavie Le Jean, Malika Chassan, Laurent Drapeau, Mireille Huc.

Maintainer: M. Huc <mireille.huc@cesbio.cnes.fr>

[1] J. P. Crutchfield and B. S. McNamara, 1987.
Equations of motion from a data series,
Complex Systems. 1, 417-452.

[2] Gouesbet G., Letellier C., 1994.
Global vector-field reconstruction by using a multivariate
polynomial L2 approximation on nets,
Physical Review E, 49 (6), 4955-4972.

[3] C. Letellier, L. Le Sceller, E. Marechal, P. Dutertre, B. Maheu,
G. Gouesbet, Z. Fei, and J. L. Hudson, 1995.
Global vector field reconstruction from a chaotic experimental
signal in copper electrodissolution,
Physical Review E, 51, 4262-4266.

[4] L. A. Aguirre & C. Letellier,
Modeling nonlinear dynamics and chaos: A review,
Mathematical Problems in Engineering, 2009, 238960.

C. Letellier, L. Le Sceller, E. Marechal, P. Dutertre, B. Maheu,
G. Gouesbet, Z. Fei, and J. L. Hudson, 1995.
Global vector field reconstruction from a chaotic experimental
signal in copper electrodissolution,
Physical Review E 51, 4262-4266.

[5] J. Maquet, C. Letellier, and L. A. Aguirre, 2007.
Global models from the Canadian Lynx cycles as a first evidence
for chaos in real ecosystems,
Juornal of Mathematical Biology. 55(1), 21-39.

[6] Mangiarotti S., Coudret R., Drapeau L., & Jarlan L., 2012.
Polynomial search and global modeling : Two algorithms for
modeling chaos,
Physical Review E, 86, 046205.

[7] Mangiarotti S., Drapeau L. & Letellier C., 2014.
Two chaotic models for cereal crops observed from satellite in
northern Morocco.
Chaos, 24(2), 023130.

[8] Mangiarotti S., 2015. Low dimensional chaotic models for the
plague epidemic in Bombay (1896-1911).
Chaos, Solitons and Fractals, 81A, 184-186.

[9] Mangiarotti S., Peyre M. & Huc M.,
A chaotic model for the epidemic of Ebola Virus Disease in West Africa (2013-2016).
Chaos, 26, 113112, 2016.

[10] Mangiarotti S., 2014. Modelisation globale et Caracterisation
Topologique de dynamiques environnementales - de l'analyse des
enveloppes fluides et du couvert de surface de la Terre a la
caracterisation topolodynamique du chaos.
Habilitation to Direct Research,
University of Toulouse 3, France.

[11] Mangiarotti S., Sharma A.K., Corgne S., Hubert-Moy L., Ruiz L., Sekhar M., Kerr Y.,
Can the global modelling technique be used for crop classification?
Chaos, Solitons & Fractals, in press.

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