Lorenz Equations

Abstract

In his historical paper, published in 1963, Lorenz [31] derived, from a model of fluid convection, a three-parameter family of three ordinary differential equations that appeared, when integrated numerically, to have extremely complicated solutions. In particular, he discovered that all nonperiodic solutions of his deterministic model were bounded but showed irregular fluctuations. Thirty years later [32] he described how he

had come across a phenomenon that later came to be called “chaos”— —seemingly random and unpredictable behavior that nevertheless proceeds according to precise and often easily expressed rules.