Difference between revisions of "Lorenz"
From TheAnalogThing
| Line 4: | Line 4: | ||
x'=σ(y-x)<br> | x'=σ(y-x)<br> | ||
| + | y'=x(ρ-z)-y<br> | ||
| + | z'=xy-βz<br> | ||
Revision as of 10:50, 1 September 2021
In 1963 Edward Norton Lorenz (23.05.1917 - 16.04.2008) developed a model for atmospheric convection (see https://journals.ametsoc.org/view/journals/atsc/20/2/1520-0469_1963_020_0130_dnf_2_0_co_2.xml and https://www.math.uni-hamburg.de/home/lauterbach/scripts/seminar03/prill.pdf for more details). This model, which was simulated on a tiny digital computer (Royal McBee LPG-30), showed an interesting behaviour which gave rise to research on chaotic attractors.
The system itself is described by three couple differential equations (x' denotes the first derivative of x with respect to time here - more typically it would be written with a dot over the variable name):
x'=σ(y-x)
y'=x(ρ-z)-y
z'=xy-βz
