The One- and Two-Dimensional Fokker-Planck Equation

  • Wolfgang Tschacher
  • Hermann Haken


The Fokker-Planck model of psychotherapy can be developed in one or two dimensions. We put forward minimal models for both cases. In the one-dimensional minimal model, we formalize how the therapist can influence client states. We use the slaving principle of synergetics, which claims that slow variables entrain (i.e., “enslave”) the behavior of the quick variables during pattern formation. Applied to therapist and client, this means that the therapist should be “slow,” i.e., have long relaxation times. This is consistent with findings of psychotherapy research suggesting that resilient, stable, and nonjudgmental therapists are actually more effective. In our model, therapist personality has an essential impact of client states. Preferably, the therapist should not be overly influenced by random events, and the coupling of the client to the therapist should be higher than vice versa. The two-dimensional minimal model allows modeling the therapist-client relationship by a limit cycle, i.e., a periodic attractor. This model dispenses with the slaving principle and allows for both oscillations and synchronized phase-shifted coupling of therapist and client behavior, thus linking the theoretical model with empirical findings on interactional synchrony. Synchrony research often applies cross-correlational methods, and we give a short summary of this research. The phase shift of the minimal model can be related to the empirically found cross-correlations. We conclude the structural-mathematical modeling of the process of psychotherapy by a two-dimensional Fokker-Planck equation.


  1. Bergomi, C., Tschacher, W., & Kupper, Z. (2013). The assessment of mindfulness with self-report measures: Existing scales and open issues. Mindfulness, 4, 191–202.CrossRefGoogle Scholar
  2. Costa, P. T., & McCrae, R. R. (1992). Revised NEO Personality Inventory (NEO PI-R) and NEO five factor inventory. Professional manual. Odessa, FL: Psychological Assessment Resources.Google Scholar
  3. Coutinho, J., Oliveira-Silva, P., Fernandes, E., Goncalves, O., Correia, D., Perrone McGovern, K., & Tschacher, W. (2018). Psychophysiological synchrony during verbal interaction in romantic relationships. Family Process.
  4. Gibson, J. J. (1979). The ecological approach to visual perception. Boston, MA: Houghton Mifflin.Google Scholar
  5. Grammer, K., Honda, R., Schmitt, A., & Jütte, A. (1999). Fuzziness of nonverbal courtship communication unblurred by motion energy detection. Journal of Personality and Social Psychology, 77, 487–508.CrossRefGoogle Scholar
  6. Haken, H. (1977). Synergetics — An introduction. Nonequilibrium phase-transitions and self-organization in physics, chemistry and biology. Berlin, Germany: Springer.Google Scholar
  7. Jirsa, V. K., Stacey, W. C., Quilichini, P. P., Ivanov, A. I., & Bernard, C. (2014). On the nature of seizure dynamics. Brain, 137, 2210–2230.CrossRefGoogle Scholar
  8. Karvonen, A., Kykyri, V.-L., Kaartinen, J., Penttonen, M., & Seikkula, J. (2016). Sympathetic nervous system synchrony in couple therapy. Journal of Marital and Family Therapy, 42, 383–395.CrossRefGoogle Scholar
  9. Koole, S. L., & Tschacher, W. (2016). Synchrony in psychotherapy: A review and an integrative framework for the therapeutic alliance. Frontiers in Psychology, 77(862). Scholar
  10. Kupper, Z., Ramseyer, F., Hoffmann, H., & Tschacher, W. (2015). Nonverbal synchrony in social interactions of patients with schizophrenia indicates socio-communicative deficits. PLoS ONE, 10(12), e0145882. Scholar
  11. Lewin, K. (1936). Principles of topological psychology. New York, NY: McGraw-Hill.CrossRefGoogle Scholar
  12. Lorenz, E. N. (1963). Deterministic non-periodic flow. Journal of the Atmospheric Sciences, 20, 130–141.CrossRefGoogle Scholar
  13. Lutz, W., & Barkham, M. (2015). Therapist effects. In R. L. Cautin & S. O. Lilienfeld (Eds.), The encyclopedia of clinical psychology (pp. 1–6). Hoboken, NJ: Wiley.Google Scholar
  14. Mandelbrot, B. (1982). The fractal geometry of nature. New York, NY: Freeman.Google Scholar
  15. Orlinsky, D. E., Grawe, K., & Parks, K. B. (1994). Process and outcome in psychotherapy – Noch einmal. In A. E. Bergin & S. L. Garfield (Eds.), Handbook of psychotherapy and behavior change (pp. 270–376). New York, NY: Wiley.Google Scholar
  16. Paulick, J., Deisenhofer, A.-K., Ramseyer, F., Tschacher, W., Rubel, J., & Lutz, W. (2018). Nonverbal Synchrony: A new approach to understand psychotherapeutic processes and drop-out. Journal of Psychotherapy Integration, 28, 367–384.CrossRefGoogle Scholar
  17. Pereira, J.-A., Barkham, M., Kellett, S., & Saxon, D. (2017). The role of practitioner resilience and mindfulness in effective practice: A practice-based feasibility study. Administration and Policy in Mental Health and Mental Health Services Research, 44, 691–704. Scholar
  18. Ramseyer, F., & Tschacher, W. (2011). Nonverbal synchrony in psychotherapy: Coordinated body-movement reflects relationship quality and outcome. Journal of Consulting and Clinical Psychology, 79, 284–295.CrossRefGoogle Scholar
  19. Ramseyer, F., & Tschacher, W. (2016). Movement coordination in psychotherapy: Synchrony of hand movements is associated with session outcome. A single-case study. Nonlinear Dynamics, Psychology, and Life Sciences, 20, 145–166.PubMedGoogle Scholar
  20. Reich, C. M., Berman, J. S., Dale, R., & Levitt, H. M. (2014). Vocal synchrony in psychotherapy. Journal of Social and Clinical Psychology, 33, 481–494.CrossRefGoogle Scholar
  21. Rössler, O. (1976). An equation for continuous chaos. Physics Letters, 57A, 397–398.CrossRefGoogle Scholar
  22. Salvatore, S., & Tschacher, W. (2012). Time dependency of psychotherapeutic exchanges: The contribution of the theory of dynamic systems in analyzing process. Frontiers in Psychology, 3(253). Scholar
  23. Tschacher, W. (1997). Prozessgestalten. Die Anwendung der Selbstorganisationstheorie und der Theorie dynamischer Systeme auf Probleme der Psychologie. Göttingen, Germany: Hogrefe.Google Scholar
  24. Tschacher, W., & Ramseyer, F. (2009). Modeling psychotherapy process by time-series panel analysis (TSPA). Psychotherapy Research, 19, 469–481.CrossRefGoogle Scholar
  25. Tschacher, W., Ramseyer, F., & Koole, S. L. (2018). Sharing the now in the social present: Duration of nonverbal synchrony is linked with personality. Journal of Personality, 86, 129–138.CrossRefGoogle Scholar
  26. Tschacher, W., Rees, G. M., & Ramseyer, F. (2014). Nonverbal synchrony and affect in dyadic interactions. Frontiers in Psychology, 5(1323). Scholar
  27. Walther, S., Ramseyer, F., Horn, H., Strik, W., & Tschacher, W. (2014). Less structured movement patterns predict severity of positive syndrome, excitement, and disorganization. Schizophrenia Bulletin, 40, 585–591.CrossRefGoogle Scholar
  28. Zhang, Y., Meng, T., Hou, Y., Pan, Y., & Hu, Y. (2018). Interpersonal brain synchronization associated with working alliance during psychological counseling. Psychiatry Research: Neuroimaging, 282, 103–109.CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Wolfgang Tschacher
    • 1
    • 2
  • Hermann Haken
    • 3
  1. 1.Universitätsklinik für Psychiatrie und PsychotherapieUniversitäre Psychiatrische, Dienste BernBernSwitzerland
  2. 2.Freiburg Institute for Advanced Studies (FRIAS)Universität FreiburgFreiburgGermany
  3. 3.Institut für Theoretische Physik und SynergetikUniversität StuttgartStuttgartGermany

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