Time Evolution of Local Complexity Measures and Aperiodic Perturbations of Nonlinear Dynamical Systems
We discuss numerical algorithms for estimating dimensional complexity of observed time-series with special emphasis on biological and medical applications. Factors which enter the procedure are discussed and applied to local estimates of pointwise dimensions or crowding indices. We illustrate the concepts with the help of experimental time-series obtained from speech signals. The temporal evolution of the crowding index shows oscillations which can be correlated with properties of the time-series. We compare the time evolution of the dimensional complexity parameter with the original time-series and also with recurrence plots of the embedded time series.
Besides the analysis of spontaneous activity of biological systems it is often more useful to study event related potentials. We have generalized our analysis code in a way that attractors can also be reconstructed from such non contiguous signals. Finally we discuss the possibility of nonlinear, aperiodic stimulation of nonlinear and chaotic systems as a method for very selective excitations of specific nonlinear modes. We discuss possible applications of this method to habituation phenomena and diagnostic use in connection with event-related potentials.
KeywordsChaotic System Speech Signal Reference Vector Recurrence Plot Dimensional Complexity
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