Difference between revisions of "Lorenz equations"
From Encyclopedia of Mathematics
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''Lorenz system'' | ''Lorenz system'' | ||
The system of equations | The system of equations | ||
| − | + | $$ | |
| + | \begin{eqnarray*} | ||
| + | \dot x &=& -\sigma x+\sigma y, \\ | ||
| − | + | \dot y &=& rx-y-xz, \\ | |
| − | + | \dot z &=& -bz+xy. | |
| + | \end{eqnarray*} | ||
| + | $$ | ||
| − | It arises as the | + | It arises as the $3$-mode truncation of the two-dimensional [[Convection equations|convection equations]] for parallel horizontal walls at constant, but different, temperatures. |
See [[Lorenz attractor|Lorenz attractor]] for more details and references; see, e.g., [[#References|[a2]]] for a picture. | See [[Lorenz attractor|Lorenz attractor]] for more details and references; see, e.g., [[#References|[a2]]] for a picture. | ||
Latest revision as of 03:05, 22 June 2022
Lorenz system
The system of equations
$$ \begin{eqnarray*} \dot x &=& -\sigma x+\sigma y, \\ \dot y &=& rx-y-xz, \\ \dot z &=& -bz+xy. \end{eqnarray*} $$
It arises as the $3$-mode truncation of the two-dimensional convection equations for parallel horizontal walls at constant, but different, temperatures.
See Lorenz attractor for more details and references; see, e.g., [a2] for a picture.
References
| [a1] | Yu.I. Neimark, P.S. Landa, "Stochastic and chaotic oscillations" , Kluwer Acad. Publ. (1992) (In Russian) |
| [a2] | H.G. Schuster, "Deterministic chaos. An introduction" , VCH (1988) |
| [a3] | C. Sparrow, "The Lorenz equations: bifurcations, chaos, and strange attractors" , Springer (1982) |
| [a4] | J.M.T. Thompson, H.B. Stewart, "Nonlinear dynamics and chaos" , Wiley (1986) pp. Chapt. 11 |
How to Cite This Entry:
Lorenz equations. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Lorenz_equations&oldid=11614
Lorenz equations. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Lorenz_equations&oldid=11614
This article was adapted from an original article by M. Hazewinkel (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article