= Lorenz system
{c}
{title2=$\dot x=\sigma(y-x),\quad\dot y=x(\rho-z)-y,\quad\dot z=xy-\beta z$}
The Lorenz system is a three-variable <autonomous differential equation> modeling an idealized <thermal convection> flow. In Edward N. Lorenz's "Deterministic Nonperiodic Flow" (1963), published in the Journal of the Atmospheric Sciences 20, pp. 130–141, numerical solutions of the model illustrated nonrepeating motion and instability to changes in the <initial condition>. Lorenz used this example to examine obstacles to very-long-range <weather forecasting>.https://samizdat.co/works/do-while/lorenz-1963.pdf[Lorenz's original 1963 paper]{ref}
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