New method for determining the largest Liapunov exponent of simple nonlinear systems

Abstract

A new method is introduced which allows a direct measurement of the largest positive or negative Liapunov exponent ${\ensuremath{\lambda}}_{m}$ of simple dynamical systems. It is shown that ${\ensuremath{\lambda}}_{m}$ can be determined experimentally by varying the coupling between two equal systems and observing the mutual correlation of their motions. An electronically simulated driven pendulum is studied as an example. The measured values of ${\ensuremath{\lambda}}_{m}$ agree well with results obtained by other methods. The method can only be applied to systems for which one knows the variables in phase span, and for which the coupling can be realized experimentally.