Advertisement

Analyzing Spatio-Temporal Patterns of Complex Systems

  • R. Friedrich
  • V. K. Jirsa
  • H. Haken
  • C. Uhl

Abstract

Rapid progress in the field of noninvasive imaging methods in medicine will provide huge amounts of data sets in the nearest future. Especially imaging methods with high time resolutions like multivariate measurements of the electroencephalogram (EEG) or the magnetoencephalogram (MEG) will allow for a detailed documentation of spatio-temporal processes in biological systems. Therefore, it is of extreme importance to develop methods which allow for a characterization and classification of spatio-temporal processes with special emphasis on medical applications.

Keywords

State Vector Spatial Mode Stimulus Frequency Brain Signal Macroscopic Description 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    H. Haken: Synergetics. An Introduction. Springer-Verlag, Berlin, Heidelberg, 1983Google Scholar
  2. [2]
    H. Haken: Advanced Synergetics. Springer-Verlag, Berlin, Heidelberg, 1987Google Scholar
  3. [3]
    H. Haken: Information and Selforganization. Springer-Verlag, Berlin, Heidelberg, 1988Google Scholar
  4. [4]
    S. Yigitbasi: Theorie inertialer Mannigfaltigkeiten und ihre Anwendung auf den Laser, Dissertation, Stuttgart 1995Google Scholar
  5. [5]
    C. Uhl, R. Friedrich, H. Haken: Reconstruction of spatio-temporal signals of complex systems, Z. Phys. B 92, 211–219 (1993s)ADSCrossRefGoogle Scholar
  6. [6]
    C. Uhl, R. Friedrich, H. Haken: Analysis of spatiotemporal signals of complex systems, Phys. Rev. E 51, 3890 (1995)ADSCrossRefGoogle Scholar
  7. [7]
    Nunez P.L.: Neocortical Dynamics and Human EEG Rhythms. Oxford University Press, Oxford, 1995Google Scholar
  8. [8]
    Wilson H.R., Cowan J.D.: Excitatory and inhibitory interactions in localized populations of model neurons. Biophys. J. 12, pp. 1–24 (1972)ADSCrossRefGoogle Scholar
  9. [8a]
    Wilson H.R., Cowan J.D.: A mathematical theory of the functional dynamics of cortical and thalamic nervous tissue. Kybernetik 13, 55–80 (1973)MATHCrossRefGoogle Scholar
  10. [9]
    Braitenberg V., Schiiz A.: Anatomy of the Cortex. Statistics and Geometry. Springer, Berlin, Heidelberg, 1991Google Scholar
  11. [10]
    Abeles M.: Corticonics. Cambridge University Press, Cambridge, 1991Google Scholar
  12. [11]
    Freeman W.J.: Tutorial on neurobiology: from single neurons to brain chaos, Intl. J. of Bifurcation and Chaos, 2 451–482 (1992)MATHCrossRefGoogle Scholar
  13. [12]
    Beurle R.L.: Properties of a mass of cells capable of regenerating pulses. Philos. Trans. Soc. London, Ser. A 240, 55–94Google Scholar
  14. [13]
    Griffith J.S.: A field theory of neural nets I: Derivation of field equations. Bull. Math. Biophys. 25, 111–120 (1963)MathSciNetMATHCrossRefGoogle Scholar
  15. [13a]Griffith J.S.: A field theory of neural nets II: Properties of field equations. Bull. Math. Biophys. 27, 187–195 (1965)MathSciNetMATHCrossRefGoogle Scholar
  16. [14]
    Kelso J.A.S., Bressler S.L., Buchanan S., DeGuzman G.C., Ding M., Fuchs A., Holroyd T.: A phase transition in human brain and behavior. Phys. Lett. A 169, 134–144 (1992)ADSCrossRefGoogle Scholar
  17. [15]
    Fuchs A., Kelso J.A.S., Haken H.: Phase transitions in the human brain: spatial mode dynamics. Intl. J. of Bifurcation and Chaos 2, 917–939 (1992)MATHCrossRefGoogle Scholar
  18. [16]
    V.K. Jirsa, R. Friedrich, H. Haken, J.A.S. Kelso: A theoretical model of phase transitions in the human brain. Biol. Cybern. 71, 27–35 (1994)MATHCrossRefGoogle Scholar
  19. [16a]V.K. Jirsa, R. Friedrich, H. Haken: Reconstruction of the spatio-temporal dynamics of a human magnetoencephalogram. Physica D 89, 100–122 (1995)MATHCrossRefGoogle Scholar
  20. [17]
    V.K. Jirsa, H. Haken, A derivation of a macroscopic field theory of the brain from the quasi-microscopic neural dynamics. To be publishedGoogle Scholar
  21. [18]
    R. Friedrich, C. Uhl: Spatio-temporal analysis of human electroencephalograms: Petit-mal epilepsy. Physica D 98, 171–182 (1996)MATHCrossRefGoogle Scholar
  22. [19]
    L.P. Shil’nikov: A case of the existence of a countable number of periodic motions. Sov. Math. Dokl. 6, 163–166 (1965); Math. USSR Sbornik 10, 91 (1970)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • R. Friedrich
  • V. K. Jirsa
  • H. Haken
    • 1
  • C. Uhl
    • 2
  1. 1.Institute of Theoretical Physics and SynergeticsUniversity of StuttgartStuttgartGermany
  2. 2.Max-Planck-Insitute of Cognitive NeuroscienceLeipzigGermany

Personalised recommendations