The 84 Lorenz system
04/06/2009
This system is made of three ordinary differential equations
\[$
\left\{
\begin{array}{l}
\dot{x} = -y^2 -z^2 -ax + aF \\[0.2cm]
\dot{y} = xy -bxz -y + G \\[0.2cm]
\dot{z} = bxy +xz -z
\end{array}
\right.
$\]
The parameters are chosen such as \(XALATEXI0X\) [1]. This system
has as a solution a fairly complicated attractor, shown in (Fig. 2).
Fig. 2 : Chaotic attractor solution to the 84 Lorenz system.
Data from the 84 Lorenz system.
A data set can be downloaded. There are three columns for x, y and z, respectively.
In addition to its quite complex dynamics, this system is characterized by the low observability coefficients
\(XALATEXI1X\),
\(XALATEXI2X\),
\(XALATEXI3X\),
that is, the dynamical variables can be ranked as
according to the observability of the attractor they provide.
[1] E. N. Lorenz, Irregularity : a fundamental property of the
atmosphere, Tellus A, 36, 98-110, 1984.
Documents
Data from the 84 Lorenz system.
Zip · 320.3 kio
ATOMOSYD {2007} |
![Suivre la vie du site]()
|
|
MàJ . 02/05/2026
|
MàJ . 02/05/2026