Studying chaotic systems using microcomputer simulations and Lyapunov exponents

The study of nonlinear systems in an undergraduate setting has become important, and this article describes the use of an interactive simulation in introducing students to the new techniques used to characterize deterministic chaos. Lyapunov exponents are introduced with emphasis on their physical significance. The results of numerical experiments on the driven, damped, Duffing two-well oscillator are reported and the global behavior of the Lyapunov exponent spectra is presented. The results confirm an important sum rule satisfied by the Lyapunov exponent spectra. Interesting, structured behavior of the Lyapunov exponent spectra is observed as the Duffing oscillator system follows the period-doubling route to chaos.