Lorenz equations
From Encyclopedia of Mathematics
Lorenz system
The system of equations
$$\dot x=-\sigma x+\sigma y,$$
$$\dot y=rx-y-xz,$$
$$\dot z=-bz+xy.$$
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