ABSTRACT

Chaos theory is the study of unstable aperiodic behavior in deterministic nonlinear

dynamic systems (Kellert 1993). It stems partially from the discovery of Edward Lorenz, a meteorologist at MIT. In 1960, when Lorenz simulated weather patterns on a computer,

he found that a small change in the initial condition produced a remarkable deviation in

the simulation results (Lorenz 1963). Figure 4.1 illustrates Lorenz’s model in the three-

dimensional state space (equations representing this model will be described later in this

section). Because the attractor (a set of data describing the evolution of a dynamic system over a sufficiently long time) of Lorenz’s system looks like a butterfly, Lorenz’s model

has been well known as the “butterfly effect” and is often used to illustrate the

complexity and unpredictability of nonlinear dynamics. The butterfly effect technically

reflects the essence of chaos, i.e., its sensitive dependence on initial conditions. In

meteorology it reflects how small changes in the initial condition can cause large changes

in the atmospheric motion. For example, a butterfly flapping its wings somewhere in

Shanghai may result in a tornado in Florida. This is also known as the butterfly effect. Therefore, long-term weather forecasting becomes impossible.