Autocorrelation Function and Mutual Information from Short Experimental Time Series

A nonlinear dynamics of self-generated current oscillations in semi-insulating GaAs was studied by the reconstruction of an attractor from a short (14500 points) time series. Two methods of choosing of a time constant (τ) for this reconstruction are compared. One of them assumes τ to be an argument of the first zero of the autocorrelation function and the other takes τ as an argument of the first minimum of the mutual information. It is shown that for periodic oscillations both methods are equivalent, but for chaotic ones only the mutual information gives a time constant which does not depend on a time series used for calculations.