Filtering for chaos

A nonlinear digital filtering approach to the problem of tracing the changing chaotic features of a nonstationary time series is proposed. The filters are based on nonlinear models whose dynamics are conditioned on the value of a parameter in the model. The dynamical behaviour can be asymptotically stable, periodic, or chaotic depending upon the parameter value. Over a critical range of values of the parameter the model is sensitively dependent on initial conditions and as a consequence the output behaviour becomes increasingly chaotic as the parameter value increases over this range. Filtering for chaos is a nonlinear autoregressive procedure for estimating this parameter as a basis for tracking changes in the chaotic dynamical behaviour of a nonstationary time series such as the EEG.<>