Definition:Lorenz Attractor
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Definition
The Lorenz attractor is a strange attractor contained in $3$-dimensional space under the flow which is the solution set to the Lorenz equations:
| \(\ds \dfrac {\d x} {\d t}\) | \(=\) | \(\ds 10 \paren {y - x}\) | ||||||||||||
| \(\ds \dfrac {\d y} {\d t}\) | \(=\) | \(\ds -x z + 28 x - y\) | ||||||||||||
| \(\ds \dfrac {\d z} {\d t}\) | \(=\) | \(\ds x y - \dfrac 8 3 z\) |
Also see
- Results about the Lorenz attractor can be found here.
Source of Name
This entry was named for Edward Norton Lorenz.
Historical Note
The Lorenz attractor was originally studied in $1963$ by Edward Norton Lorenz as a model for weather.
In $2002$ it was demonstrated by Warwick Tucker to be a strange attractor.
Sources
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): chaos
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): chaos