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[edit]

[a1] |  Yu.I. Neimark, P.S. Landa, "Stochastic and chaotic oscillations" , Kluwer Acad. Publ. (1992) (In Russian)

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[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