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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.
Zip - 320.2 ko
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
4139 - 12/12/19

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