GPoM.FDLyapu-package: GPoM.FDLyapu package: Lyapunov Exponents and Kaplan-Yorke...
In GPoM.FDLyapu: Lyapunov Exponents and Kaplan-Yorke Dimension
Description
Note
Author(s)
References
Description
Estimation of the spectrum of Lyapunov Exponents and the Kaplan-Yorke
dimension of any low-dimensional model of polynomial form.
It can be applied, for example, to systems such as the chaotic
Lorenz-1963 system or the hyperchaotic Rossler-1979 system.
It can also be applied to dynamical models in Ordinary Differential Equations
(ODEs) directly obtained from observational time series using the 'GPoM' package. The used approach
is semi-formal, the Jacobian matrix being estimated automatically from the polynomial equations.
Two methods are made available : one introduced by Wolf et al. (1985) [1]
and the other one by Grond et al. (2003) [2].
Note
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 Défi InFiNiTi (CNRS) and PNTS
are also acknowledged (projects Crops'IChaos and Musc & SlowFast).
Author(s)
Sylvain Mangiarotti, Mireille Huc.
Maintainer: M. Huc <mireille.huc@cesbio.cnes.fr>
References
[1] A. Wolf, J. B. Swift, H. L. Swinney & J. A. Vastano,
Determining Lyapunov exponents from a time series,
Physica D, 285-317, 1985.
[2] F. Grond, H. H. Diebner, S. Sahle, A. Mathias, S. Fischer,
O. E. Rossler, A robust, locally interpretable algorithm for
Lyapunov exponents, Chaos, Solitons \& Fractals, 16, 841-852 (2003).
GPoM.FDLyapu documentation built on Aug. 29, 2019, 5:05 p.m.
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Description Note Author(s) References
Description
Estimation of the spectrum of Lyapunov Exponents and the Kaplan-Yorke dimension of any low-dimensional model of polynomial form. It can be applied, for example, to systems such as the chaotic Lorenz-1963 system or the hyperchaotic Rossler-1979 system. It can also be applied to dynamical models in Ordinary Differential Equations (ODEs) directly obtained from observational time series using the 'GPoM' package. The used approach is semi-formal, the Jacobian matrix being estimated automatically from the polynomial equations. Two methods are made available : one introduced by Wolf et al. (1985) [1] and the other one by Grond et al. (2003) [2].
Note
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 Défi InFiNiTi (CNRS) and PNTS
are also acknowledged (projects Crops'IChaos and Musc & SlowFast).
Author(s)
Sylvain Mangiarotti, Mireille Huc.
Maintainer: M. Huc <mireille.huc@cesbio.cnes.fr>
References
[1] A. Wolf, J. B. Swift, H. L. Swinney & J. A. Vastano,
Determining Lyapunov exponents from a time series,
Physica D, 285-317, 1985.
[2] F. Grond, H. H. Diebner, S. Sahle, A. Mathias, S. Fischer,
O. E. Rossler, A robust, locally interpretable algorithm for
Lyapunov exponents, Chaos, Solitons \& Fractals, 16, 841-852 (2003).
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