Detection of nonlinear dynamics in short, noisy time series

THE accurate identification of deterministic dynamics in an experimentally obtained time series(1-5) can lead to new insights regarding underlying physical processes, or enable prediction, at least on short timescales. But deterministic chaos arising from a nonlinear dynamical system can easily be mistaken for random noise(6-8). Available methods to distinguish deterministic chaos from noise can be quite effective, but their performance depends on the availability of long data sets, and is severely degraded by measurement noise. Moreover, such methods are often incapable of detecting chaos in the presence of strong periodicity, which tends to hide underlying fractal structures(9). Here we present a computational procedure, based on a comparison of the prediction power of linear and nonlinear models of the Volterra-Wiener form(10), which is capable of robust and highly sensitive statistical detection of deterministic dynamics, including chaotic dynamics, in experimental time series. This method is superior to other techniques(1-6,11,12) when applied to short time series, either continuous or discrete, even when heavily contaminated with noise, or in the presence of strong periodicity.