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.

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