Lorenz System - Overview

Overview

In 1963, Edward Lorenz developed a simplified mathematical model for atmospheric convection. The model is a system of three ordinary differential equations now known as the Lorenz equations:

$\begin{align} \frac{\mathrm{d}x}{\mathrm{d}t} &= \sigma (y - x), \\ \frac{\mathrm{d}y}{\mathrm{d}t} &= x (\rho - z) - y, \\ \frac{\mathrm{d}z}{\mathrm{d}t} &= x y - \beta z. \end{align}$

Here, and make up the system state, is time, and, are the system parameters. The Lorenz equations also arise in simplified models for lasers, dynamos, thermosyphons, brushless DC motors, electric circuits, and chemical reactions.

From a technical standpoint, the Lorenz system is nonlinear, three-dimensional and deterministic. The Lorenz equations have been the subject of at least one book length study.

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