Dynamical Systems and the Development of Schizophrenic Symptoms — An Approach to a Formalization

  • Brigitte Ambühl
  • Rudolf Dünki
  • Luc Ciompi
Part of the Springer Series in Synergetics book series (SSSYN, volume 58)


Based on the hypothesis of irregular dynamics in the evolution of schizophrenia (Ciompi et al., 1991), we explored the possibility of describing these processes in terms of dynamical systems (chaos) theory. By analyzing time series of a single schizophrenic patient we found support for the existence of a strange attractor. A short discussion of methods (Grassberger-Procaccia algorithm) that can be applied to dynamical systems completes the theoretical part. This formalization is a basis for further experimental studies as well as for testing and developing models and simulations.


Autocorrelation Function Psychotic Symptom Strange Attractor Daily Fluctuation Theoretical Part 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. ABRAHAM, N.B., ALBANO, A.M., DAS, B., GUZMAN de, G., YONG, S., GIOGGIA, R.S., PUCCIONI, G.P. & TREDICCE, J.R. 1986. Calculating the dimensions of attractors from small data sets. Phys. Lett. A, 114, p. 127.CrossRefGoogle Scholar
  2. AEBI, E. & CIOMPI, L. 1989. Everyday Events and the Temporal Course of Daily Fluctuations of Psychotic Symptoms. Schizophrenia Research, Vol. 2, Nos. 1–2.CrossRefGoogle Scholar
  3. AEBI, E., REVENSTORF, D. & ACKERMANN, K. 1989. A Concept of Optimal Social Stimulation in Acute Schizophrenia — Time Series Analysis of Psychotic Behavior. The Third European Conference on Psychotherapy Research, Berne, September 5–9.Google Scholar
  4. ATTEN, P., CAPUTO, J.G., MALRAISON, B. & GAGNE, Y. 1984. Détermination de dimension d’attracteurs pour différent écoulements. J. Méc. Théor. Appl. Numéro spécial, p. 133.Google Scholar
  5. CIOMPI, L. 1991. Affects as Central Organising and Integrating Factors. A New Psychosocial/Biological Model of the Psyche. British Journal of Psychiatry, 159, 57–105.CrossRefGoogle Scholar
  6. CIOMPI, L. & MüLLER, C. 1976. Lebensweg und Alter der Schizophrenen. Berlin: Springer.Google Scholar
  7. CIOMPI, L., DAUWALDER, H.P., MAIER, Ch., AEBI, E., Trütsch, K., Kupper, Z. & Ruthishauser, Ch. 1990. The pilot project “Soteria Berne”. Clinical experiences and preliminary results. Lecture presented at the Third International Schizophrenia Symposium. Berne.Google Scholar
  8. CIOMPI, L. AMBüHL, B., DüNKI, R.M., THOMAS, R. 1991 (in press). Schizophrenia and Chaos Theory. Exploratory Investigations in the Dynamics of Complex Psycho-Socio-Biological Systems.Google Scholar
  9. DüNKI, R.M. 1991 (in press). The estimation of the Kolmogorov entropy from time series and its limitations when performed on EEG. Bulletin of mathematical biology.Google Scholar
  10. ECKMANN, J.P. 1981. Roads to turbulence in dissipative dynamical systems. Rev. Mod. Phys., 53, p. 643.MathSciNetADSzbMATHCrossRefGoogle Scholar
  11. GRASSBERGER, P. & PROCACCIA, I. 1983. Characterization of strange attractors. Phys Rev. Lett, 50, p. 346.MathSciNetADSCrossRefGoogle Scholar
  12. GREBOGI, C., OTT, E., PELIKAN, S. & YORKE, J.A. 1984. Strange attractors that are not chaotic. Physica 13D, p. 261.MathSciNetADSGoogle Scholar
  13. HUBSCHMID, T. & AEBI, E. 1986. Berufliche Wiedereingliederung von psychiatrischen Langzeitpatienten. Soc. Psychiatry, 21, 152–157.CrossRefGoogle Scholar
  14. SCHUSTER, H.G. 1989. Deterministic Chaos. An Introduction. Weinheim: Verlagsgesellschaft mbH.zbMATHGoogle Scholar
  15. SHAW, R.S. 1981. Strange Attractors, Chaotic Behaviour and Information Flow. Z. Naturforsch., 36a, p. 80.ADSGoogle Scholar
  16. TAKENS, F. 1981. Detecting strange attractors in turbulence. Lecture Notes in Mathematics., 898, Berlin: Springer, p. 361.Google Scholar
  17. THEILER, J. 1986. Spurious algorithms applied to limited time-series data. Phys. Rev. A, 34, p. 2427.ADSCrossRefGoogle Scholar
  18. THEILER, J. 1987. Efficient algorithm for estimating the correlation dimension from a set of discrete points. Phys. Rev. A, 36, p. 4456.MathSciNetADSCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1992

Authors and Affiliations

  • Brigitte Ambühl
  • Rudolf Dünki
  • Luc Ciompi

There are no affiliations available

Personalised recommendations