A. Namajunas et A. Tamasevicius, SIMPLE LABORATORY INSTRUMENTATION FOR MEASURING POINTWISE DIMENSIONS FROM CHAOTIC TIME-SERIES, Review of scientific instruments, 65(9), 1994, pp. 3032-3033
An analog instrumentation for estimating dimensions of chaotic dynamic
al systems has been developed. The technique employs time series of th
e Poincare points successively displayed on the screen of an oscillosc
ope. It provides a rapid way to estimate the pointwise dimension from
a single variable directly in an experiment. The instrumentation is ea
sy to build and is convenient to employ. We have tested it by applying
to periodic and quasiperiodic oscillators, and have verified by means
of the fractal two-dimensional Poincare map, simulated from the Duffi
ng-Holmes differential equation. The measured values well agree with t
he computer calculated ones.