The identification of critical fluctuations and phase transitions in short term and coarse-grained time series-a method for the real-time monitoring of human change processes.
We introduce two complementary measures for the identification of critical instabilities and fluctuations in natural time series: the degree of fluctuations F and the distribution parameter D. Both are valid measures even of short and coarse-grained data sets, as demonstrated by artificial data from the logistic map (Feigenbaum-Scenario). A comparison is made with the application of the positive Lyapunov exponent to time series and another recently developed complexity measure-the Permutation Entropy. The results justify the application of the measures within computer-based real-time monitoring systems of human change processes. Results from process-outcome research in psychotherapy and functional neuroimaging of psychotherapy processes are provided as examples for the practical and scientific applications of the proposed measures.
Schiepek
Günter
G
Institute of Synergetics and Psychotherapy Research, Paracelsus Medical University, Universitätsklinikum/Christian Doppler Klinik, Ignaz Harrer Str. 79, 5020 Salzburg, Austria. guenter.schiepek@ccsys.de
Strunk
Guido
G
D000465:Algorithms; D003198:Computer Simulation; D003936:Diagnosis, Computer-Assisted / Q000379:methods*; D019277:Entropy; D006801:Humans; D008954:Models, Biological; D017711:Nonlinear Dynamics; D015203:Reproducibility of Results; D012815:Signal Processing, Computer-Assisted; D013997:Time Factors