Synergetic Analysis of Human Electroencephalograms: Petit-Mal Epilepsy

  • R. Friedrich
  • C. Uhl
Part of the Springer Proceedings in Physics book series (SPPHY, volume 69)


The clinical diagnosis of epileptic seizures is usually based on an inspection of the electroencephalogram (EEG). The present paper is devoted to a description of a more refined analysis of EEG patterns of petit-mal epilepsy. The treatment is based on the synergetic approach to macroscopic patterns in complex systems which has been inaugurated by H. Haken. This approach aims at an understanding of both spatial as well as dynamical aspects of macroscopic EEG patterns.


Epileptic Seizure Chaotic Behaviour Unstable Manifold Homoclinic Orbit Stable Manifold 
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.


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  1. [1]
    H. Berger, ‘Über das Elektrenkephalogramm des Menschen’, Arch. Psychiatr. Nervenkr. 87, 527–570 (1929)CrossRefGoogle Scholar
  2. [2]
    J. Kugler, Elektmenzephalographie in Klinik und Praxis ( Georg Thieme-Verlag, Stuttgart, 1981 )Google Scholar
  3. [3]
    D. Lehmann, ‘Multichannel Topography of Human Alpha EEG Fields’, Electroenceph. clin. Neurophysiol. 31, 439–449 (1971)ADSGoogle Scholar
  4. D. Lehmann. Lehmann, ‘Human Scalp EEG Fields: Evoked, Alpha, Sleep, and Spike-Wave Patterns’, in, Synchronization of EEG Activity in Epilepsies, eds. H. Petsche, M.A.B. Brazier ( Springer-Verlag, Berlin, 1972 )Google Scholar
  5. [4]
    H. Haken, in Synergetics of the Brain, eds. E. Basar, H. Flohr, H. Haken, and A.J. Mandell ( Springer-Verlag, Berlin, 1983 )Google Scholar
  6. [5]
    H. Haken, Synergetics. An Introduction ( Springer-Verlag, Berlin, 1983 )MATHGoogle Scholar
  7. [6]
    H. Haken, Advanced Synergetics ( Springer-Verlag, Berlin, 1987 )Google Scholar
  8. [7]
    H. Haken, Information and Selforganization ( Springer-Verlag, Berlin, 1988 )Google Scholar
  9. [8]
    A. Babloyantz, ‘Strange Attractors in the Dynamics of Brain Activity’, in: Complex Systems - Operational Approaches, ed. H. Haken ( Springer-Verlag, Berlin, 1985 )Google Scholar
  10. A. Babloyantz, C. Nicolis, and M. Salazar, ‘Evidence of chaotic dynamics of brain activity during the sleep cycle’, Phys. Lett. A 111, 152 (1985)CrossRefGoogle Scholar
  11. A. Babloyantz and A. Destexhe, ‘Strange Attractors in the Human Cortex’, in: Temporal Disorder in Human Oscillatory Systems, eds. L. Reusing, U. an der Heiden, M.C. Mackey ( Springer-Verlag, Berlin, 1986 )Google Scholar
  12. A. Babloyantz and A. Destexhe, ‘Low-dimensional chaos in an instance of epilepsy’, Proc. Natl. Acad. Sci. 83, 3513–3517 (1986)CrossRefADSGoogle Scholar
  13. [9]
    G. Mayer-Kress and J. Holzfuss. Holzfuss, ‘Analysis of the Human Electroencephalogram with Methods from Nonlinear Dynamics’, in, Temporal Disorder in Human Oscillatory Systems, eds. L. Rensing, U. an der Heiden, M.C. Mackey ( Springer-Verlag, Berlin, 1986 )Google Scholar
  14. S.P. Layne, G. Mayer-Kress, and J. Holzfuss, ‘Problems Associated with Dimensional Analysis of Electroencephalogram Data’, in, Dimensions and Entropies in Chaotic Systems, ed. by G. Mayer-Kress, ( Springer-Verlag, Berlin, 1986 )Google Scholar
  15. [10]
    A. Fuchs, R. Friedrich, H. Haken, and D. Lehmann, ‘Spatio-Temporal Analysis of Multichannel a-EEG Map Series’, in Computational Systems - Natural and Artificial, ed. by H. Haken ( Springer-Verlag, Berlin, 1987 )Google Scholar
  16. [11]
    R. Friedrich, A. Fuchs, and H. Haken, ‘Synergetic Analysis of SpatioTemporal EEG Patterns’, in Nonlinear Wave Processes in Excitable Media, eds. A.V. Holden, M. Markus, and H.G. Othmer ( Plenum, New York, 1991 )Google Scholar
  17. [12]
    R. Friedrich, A. Fuchs, and H. Haken, ‘Modelling of Spatio-Temporal EEG Patterns’, in Mathematical approaches to brain functioning diagnostics, eds. I. Dvorak, A. V. Holden (Manchester University Press, 1991 )Google Scholar
  18. [13]
    R. Friedrich, A. Fuchs, and H. Haken,‘Spatio-Temporal EEG Patterns’, in Synergetics of Rhythms in Biological Systems, eds. H. Haken and H.P. Kópchen, ( Springer-Verlag, Berlin, 1992 )Google Scholar
  19. [14]
    C. Uhl, Diplom thesis, Stuttgart 1991Google Scholar
  20. [15]
    R. Friedrich, M. Bestehorn, H. Haken, ‘Pattern Formation in Convective Instabilities’, Int. J. Mod. Phys. B Vol. 4, No. 3 365–400 (1990)CrossRefADSMathSciNetGoogle Scholar
  21. [16]
    L.P. Shil’nikov, A case of the existence of a countable number of periodic motions’, Soy. Math. Dokl. 6, 163–166 (1965);Google Scholar
  22. L.P. Shil’nikov, ‘A case of the existence of a countable number of periodic motions’, Math. USSR Sbornik 10, 91 (1970)CrossRefMATHGoogle Scholar
  23. [17]
    A. Wunderlin, ‘On the principles of synergetics’, this volumeGoogle Scholar
  24. [18]
    P. Glendinning, C. Sparrow, ‘Local and Global Behavior near Homoclinic Orbits’, J. Stat. Phys. 35, 645–696 (1984)CrossRefMATHADSMathSciNetGoogle Scholar
  25. [19]
    E.J. Speckmann, Experimentelle Epilepsieforschung ( Wissenschaftliche Buchgesellschaft, Darmstadt, 1986 )Google Scholar
  26. [20]
    Movie Spatio-Temporal EEG Patterns,by R. Friedrich, A. Fuchs, and H. HakenGoogle Scholar
  27. [21]
    C. Elphick, E. Tirapegui, M.E. Brachet, P. Coullet, and G. Iooss, ‘A simple global characterization for normal forms of sinular vector fields’, Physics D 29, 95Google Scholar
  28. [22]
    J.P. Eckmann, D. Ruelle, ‘Fundamental Limitations for Estimating Dimensions and Lyapunov Exponents in Dynamical Systems’, preprint IHES/P/90/11Google Scholar

Copyright information

© Springer-Verlag Berlin, Heidelberg 1992

Authors and Affiliations

  • R. Friedrich
    • 1
  • C. Uhl
    • 1
  1. 1.Institute of Theoretical Physics and SynergeticsUniversity of StuttgartStuttgart 80Fed. Rep. of Germany

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