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).

$PNG - 64 ko$
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

$y \triangleright x = z$ 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 · 320.2 ko

24883 - 14/10/24

| MàJ . 04/02/2024