Lorenz63

<p>The Lorenz-1963 model is a three-dimensional model obtained
by Edouard N. Lorenz in 1963. The system reads
$dX/dt = -\sigma Y -\sigma Z$
$dY/dt = X (\rho - Z) - Y$
$dZ/dt = X Y - \beta Z$.
For $(\sigma, \rho, \beta) = (10,28,8/3)$, it produces a chaotic
behavior. The chaotic attractor reached at the convergence
has become paradigmatic of chaos.
Its formulation can be visualized using
visuEq(nVar = 4, dMax = 2, K = Lrz63$KL, approx = 2)</p>

data

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 approach used 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) <doi:10.1016/0167-2789(85)90011-9>
and the other one introduced by Grond et al. (2003) <doi:10.1016/S0960-0779(02)00479-4>.
The package is provided with an interface for a more intuitive usage,
it can also be run without the interface.
This platform is developed at the Centre d'Etudes Spatiales de la Biosphere (CESBIO),
UMR 5126 UPS/CNRS/CNES/IRD, 18 av. Edouard Belin, 31401 TOULOUSE, FRANCE.
The developments were funded by the French program Les Enveloppes Fluides
et l'Environnement (LEFE, MANU, projects GloMo, SpatioGloMo and MoMu). The
French programs Defi InFiNiTi (CNRS) and PNTS (CNRS) are also acknowledged
(projects Crops'I Chaos and Musc & SlowFast).

Mireille Huc

GPoM.FDLyapu

Lyapunov Exponents and Kaplan-Yorke Dimension

Sylvain Mangiarotti

Institut de Recherche pour le D<c3><a9>veloppement 

Centre National de la Recherche Scientifique 

Lorenz63 function

<p>An object of class <code>list</code> of length 2.</p>

Format

Lorenz-1963 system — Lorenz63

Lorenz-1963 system

Lorenz63: Lorenz-1963 system

Description

Usage

Arguments

Format

References