Lorenz Model

Model Description

This simple model was developed by Edward Lorenz in 1963 to study fluid mechanics (based on Navier-Stokes equations). It is the first ever model of a chaotic dynamical system. Chaos arises when a deterministic, nonlinear dynamical system exhibits long-term unpredictability in behavior due to sensitivity to initial conditions.

The model is a three-dimentional system of differential equations. Specifically, the model describes the convection motion of a fluid in a small idealized "Rayleigh-Benard" container. The basic presumption is that there is fluid in a container with surfaces at different temperatures. The model shows that the fluid motion eventually leads to a chaotic behavior.  When plotted in the three spatial dimensions, the dynamics of the model describe a shape called "strange attractor."

Lorenz
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