Abstract
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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Asay TP, Lambert MJ, Gregersen AT, Goates MK (2002) Using patient-refocused research in evaluating treatment outcome in private practice. J Clin Psychol 58: 1213–1225
an der Heiden U (1992) Chaos in health and disease—phenomenology and theory. In: Tschacher W, Schiepek G, Brunner EJ (eds) Self-organization and clinical psychology. Springer, Berlin, pp 55–87
Bandt C, Pompe B (2002) Permutation entropy: A natural complexity measure for time series. Phys Rev Lett 88: 174102
Eckmann JP, Oliffson Kamphorst S, Ruelle D (1987) Recurrence plots of dynamical systems. Europhys Lett 4: 973–977
Freeman WJ (2000) Emotion is essential to all intentional behaviors. In: Lewis MD, Granic I (eds) Emotion, development, and self-organisation. Dynamic systems approaches to emotional development. Cambridge University Press, Cambridge, pp 209–235
Goodman WK, Price LH, Rasmussen SA, Mazure C, Fleischmann RL, Hill CL, Heninger GR, Charney DS (1989) The Yale-Brown obsessive compulsive scale. I. Development, use, and reliability. Arch Gen Psychiatry 46: 1006–1011
Haken H (1996) Principles of brain functioning. A synergetic approach to brain activity, behavior, and cognition. Springer, Berlin
Haken H (2002) Brain dynamics. Springer, Berlin
Haken H (2004) Synergetics. Introduction and advanced topics. Springer, Berlin
Haken H, Schiepek G (2006) Synergetik in der Psychologie. Selbstorganisation verstehen und gestalten. Hogrefe, Göttingen
Hayes AM, Feldman GC, Beevers CG, Laurenceau JP, Cardaciotto LA, Lewis-Smith J (2007a) Discontinuities and cognitive changes in an exposure-based cognitive therapy for depression. J Consult Clin Psychol 75: 409–421
Hayes AM, Laurenceau JP, Feldman GC, Strauss JL, Cardaciotto LA (2007b) Change is not always linear: The study of nonlinear and discontinuous patterns of change in psychotherapy. Clin Psychol Rev 27: 715–723
Ilardi SS, Craighead WE (1994) The role of non-specific factors in cognitive-behavior therapy for depression. Clin Psychol Res Pract 1: 138–156
Kantz, H, Kurths, J, Mayer-Kress, G (eds) (1998) Non-linear analysis of physiological data. Springer, Berlin
Kelso JAS (1995) Dynamic patterns. The self-organization of brain and behavior. MIT Press, Cambridge
Kowalik ZJ, Elbert T (1995) A practical method for the measurements of the chaoticity of electric and magnetic brain activity. Int J Bifurc Chaos 5: 475–490
Kowalik ZJ, Schiepek G, Kumpf K, Roberts LE, Elbert T (1997) Psychotherapy as a chaotic process II: The application of nonlinear analysis methods on quasi time series of the client-therapist-interaction. A nonstationary approach. Psychother Res 7: 197–218
Kruse, P, Stadler, M (eds) (1995) Ambiguity in mind and nature. Multistable cognitive phenomena. Springer, Berlin
Lambert MJ, Whipple JL, Smart DW, Vermeersch DA, Nielsen SL, Hawkins EJ (2001) The effects of providing therapists with feedback on patient progress during psychotherapy: Are outcomes enhanced?. Psychother Res 11: 49–68
Lang PJ, Bradley MM, Cuthbert BN (1997/2001) International affective picture system (IAPS): Instruction manual and affective ratings. Center for research in psychophysiology. University of Florida, Gainesville
Nowak A, Vallacher RR (1998) Dynamical social psychology. Guilford Press, New York
Popovych OV, Hauptmann C, Tass PA (2006) Control of neural synchrony by nonlinear delayed feedback. Biol Cybern 95: 69–85
Rosenstein MT, Collins JJ, de Luca CJ (1993) A practical method for calculating largest Lyapunov exponents from small data sets. Physica D 65: 117–134
Schiepek G (2003) A dynamic systems approach to clinical case formulation. Eur J Psychol Assess 19: 175–184
Schiepek G, Kowalik ZJ, Schütz A, Köhler M, Richter K, Strunk G, Mühlnickel W, Elbert T (1997) Psychotherapy as a chaotic process I. Coding the client-therapist-interaction by means of sequential plan analysis and the search for chaos: A stationary approach. Psychother Res 7: 173–194
Schiepek G, Tominschek I, Karch S, Lutz J, Mulert C, Meindl T, Pogarell O (2009) A controlled single case study with repeated fMRI measures during the treatment of a patient with obsessive-compulsive disorder: Testing the nonlinear dynamics approach to psychotherapy. World J Biol Psychiatry 10: 658–668. doi:10.1080/15622970802311829
Schiepek G, Perlitz V (2009) Self-organization in clinical psychology. In: Meyer P (eds) Encyclopedia of complexity and systems science. Springer, Heidelberg, pp 7991–8009
Skinner JE, Molnar M, Tomberg C (1994) The point correlation dimension: Performance with nonstationary surrogate data and noise. Integr Physiol Behav Sci 29: 217–234
Strunk G (2005) Organisierte Komplexität. Mikroprozess-Analysen der Interaktionsdynamik zweier Psychotherapien mit den Methoden der nichtlinearen Zeitreihenanalyse. Dissertation, Otto-Friedrich-Universität Bamberg, http://www.opus-bayern.de/uni-bamberg/volltexte/2005/64/
Strunk G, Schiepek G (2006) Systemische Psychologie. Einführung in die komplexen Grundlagen menschlichen Verhaltens. Spektrum Akademischer Verlag, Heidelberg
Tominschek I, Schiepek G, Mehl C, Maier K, Heinzel S, Bauhofer C, Berbic B, Zaudig M (2008) Real-Time Monitoring in der Behandlung von Zwangsstörungen: Technologie und Fallbeispiel. Verhaltenstherapie 18: 146–152
Vetter G, Stadler M, Haynes JD (1997) Phase transitions in learning. J Mind Behav 18: 335–350
Webber CL, Zbilut JP (1994) Dynamical assessment of physiological systems and states using recurrence plot strategies. J Appl Physiol 76: 965–973
Whipple JL, Lambert MJ, Vermeersch DA, Smart DW, Nielsen SL, Hawkins EJ (2003) Improving the effects of psychotherapy: The use of early identification of treatment and problem-solving strategies in routine practice. J Couns Psychol 50: 59–68
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Schiepek, G., Strunk, G. 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. Biol Cybern 102, 197–207 (2010). https://doi.org/10.1007/s00422-009-0362-1
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00422-009-0362-1