Lorenz equations

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