The 84 Lorenz system
Christophe LETELLIER
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 \((a,b,F,G)=(0.25,4.0,8.0,1.0)\) [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
\(\eta_x^2 = 0.1\),
\(\eta_y^2 = 0.2\),
\(\eta_z^2 = 0.1\),
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.
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