Tool to recover scalar time-delay systems from experimental time series

Abstract

We propose a method that is able to analyze chaotic time series gained from experimental data. The method allows us to identify scalar time-delay systems. If the dynamics of the system under investigation is governed by a scalar time-delay differential equation of the form $\frac{\mathrm{dy}(t)}{\mathrm{dt}}=h(y(t), y(t\ensuremath{-}{\ensuremath{\tau}}_{0}))$, the delay time ${\ensuremath{\tau}}_{0}$ and the function $h$ can be recovered. There are no restrictions to the dimensionality of the chaotic attractor. It turns out that the method is not strongly sensitive to additional noise. We successfully apply the method to various time series taken from a computer experiment and two different electronic oscillators.