14 - The Lorenz System

Abstract

This chapter investigates the famous Lorenz system from meteorology. This was one of the first examples of a differential equation that was shown to exhibit chaotic behavior. Linearization provides a mechanism to understand the behavior near the equilibria of this system. Global techniques then show that there is an attractor for this system that is neither an equilibrium point nor a limit cycle. A specific model for this attractor is then constructed. This reduces the three-dimensional system of differential equations to a two-dimensional iterated function, which, in turn, is reduced to a one-dimensional mapping.