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Strange Attractor EEG as Sign of Cognitive Function

  • Erol Başar
  • C. Başar-Eroglu
  • J. Röschke
  • J. Schult

Abstract

In our earlier approaches, we used the algorithm of Grassberger and Procaccia (1983) to determine the dimensionality of brain waves. The SWS-sleep electroencephalogram (EEG) of intracranial structures of the cat brain was embedded into phase space, and the dimensions of the attractors of the cat’s cortex, hippocampus, and reticular formation were computed. The results confirmed the pioneering findings of Babloyantz et al. (1985) concerning special structures of the cat brain. They also confirmed our long-standing assumptions that the EEG represents an integrative signal stemming from deterministic processes and is a strange attractor (Basar et al., 1988; Röschke and Basar, 1988, 1989). Several authors also used this approach for the human EEG during the waking stage and especially during alpha activity (Babloyantz, 1989; Saermark et al., 1989). For a collection of papers covering this topic, see Basar (1988) and Basar and Bullock (1989). However, we did not encounter in these references any description of the correlation dimension over long periods of time and from simultaneous recordings over several locations of the human scalp EEG. Since the aim of the present study is to demonstrate that the EEG reflects properties of a quasi-deterministic brain process, we performed analysis of the correlation dimension of the human awake EEG during long periods from various locations. If the EEG is a signal stemming from quasi-deterministic neuronal processes, it should be possible to find replicable EEG states if repeatable initial conditions for a sensory-cognitive input to CNS can be realized experimentally.

Keywords

Coherent State Correlation Dimension Target Signal Strange Attractor Brain Dynamic 
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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References

  1. Abraham, R.H., Shaw, C.D. (1983): Dynamics. The geometry of behavior. Santa Cruz, CA: Ariel PressGoogle Scholar
  2. Babloyantz, A. (1988): Chaotic dynamics in brain activity. In: Dynamics of sensory and cognitive processing by the brain. Basar, E. (ed.). Berlin: Springer, pp. 196–202CrossRefGoogle Scholar
  3. Babloyantz, A. (1989): Estimation of correlation dimensions from single and multichannel recordings—a critical view. In: Brain dynamics. Progress and perspectives. Bas4r, E., Bullock, T.H. (eds.). Berlin: Springer, pp. 122–130Google Scholar
  4. Babloyantz, A., Nicolis, C., Salazar, M. (1985): Evidence of chaotic dynamics of brain activity during the sleep cycle. Phys. Lett. [A] 111, 152–156CrossRefGoogle Scholar
  5. Basşr, E. (1980): EEG-brain dynamics. Relation between EEG and brain evoked potentials. Amsterdam: Elsevier/North-HollandGoogle Scholar
  6. Basşr, E. (1983a): Synergetics of neuronal populations. A survey on experiments. In: Synergetics of the brain. Basar, E., Flohr, H., Haken, H., Mandell, A. (eds.). Berlin: Springer, pp. 183–200CrossRefGoogle Scholar
  7. Başar, E. (1983b): Toward a physical approach to integrative physiology. I: Brain dynamics and physical causality. Am. J. Physiol. 245, R510 — R533Google Scholar
  8. Başar, E. (1988): EEG-dynamics and evoked potentials in sensory and cognitive processing by the brain. In: Dynamics of sensory and cognitive processing by the brain. Basar, E. (ed.). Berlin: Springer, pp. 30–55Google Scholar
  9. Başar, E., Bullock, T.H. (1989): Brain dynamics. Progress and perspectives. Berlin: SpringerGoogle Scholar
  10. Basşr, E., Röschke, J. (1983): Synergetics of neuronal populations. A survey on experiments. In: Synergetics of the brain. Bassar, E., Flohr, H., Haken, H., Mandell, A.J. (eds.). Berlin: Springer, pp. 199–200Google Scholar
  11. Basşr, E., Basar-Eroglu, C., Rosen, B., Schutt, A. (1984): A new approach to endogenous event-related potentials in man: Relation between EEG and P300-wave. Int. J. Neurosci. 24, 1–21CrossRefGoogle Scholar
  12. Başar, E., Basar-Eroglu, C., Röschke, J. (1988): Do coherent patterns of strange attractor EEG reflect deterministic sensory-cognitive states of the brain? In: From chemical to biological organization. Markus, M., Müller, S., Nicholis, G. (eds.).Berlin: Springer, pp. 297–306Google Scholar
  13. Berger, H. (1938): Das Elektroencephalogramm des Menschen. Nova Acta Leopold. 6, 38Google Scholar
  14. Bullock, T.H. (1989): Signs of dynamic processes in organized neural tissue: Extracting order from chaotic data. In: Brain dynamics. Progress and perspectives. Bassar, E.Google Scholar
  15. Bullock, T.H. (eds.). Berlin: Springer, pp. 537–547Google Scholar
  16. Dvorak, I., Siska, J. (1986): On some problems encountered in the estimation of the correlation dimension of the EEG. Phys. Lett. A 118, 63–66Google Scholar
  17. Freeman, W.J. (1975): Mass action in the nervous system. New York: Academic Press Freeman, W.J. (1983): Dynamics of image formation by nerve cell assemblies. In: Synergetics of the brain. Bassar, E., Flohr, H., Haken, H., Mandell, A.J. (eds.). Berlin: Springer, pp. 102–121Google Scholar
  18. Freeman, W.J., Skarda, C.A. (1985): Spatial EEG patterns, non-linear dynamics and perception: The neo-Sherringtonian view. Brain Res. Rev. 10, 147–175CrossRefGoogle Scholar
  19. Grassberger, P., Procaccia, I. (1983): Measuring the strangeness of strange attractors. Physica [D] 9, 183–208Google Scholar
  20. Hillyard, S.A., Picton, T.W. (1979): Event-related brain potentials and selective information processing in man. In: Cognitive components in cerebral event-related potentials and selective attention. Desmedt, J.E. (ed.). Prog. Clin. Neurophysiol. 6, 1–52Google Scholar
  21. Kornhuber, H.H., Deecke, L. (1965): Hirnpotentialänderungen bei Willkürbewegungen and passiven Bewegungen des Menschen: Bereitschaftspotential and reafferente Potentiale. Pflügers. Arch. 284, 1–17CrossRefGoogle Scholar
  22. Layne, S.P., Mayer-Kress, G., Hozfuss, J. (1985): Problems associated with dimensional analysis of electroencephalogram data. In: Dimensions and entropies in chaotic systems. Mayer-Kress, G. (ed.). Berlin: Springer, pp. 246Google Scholar
  23. Lorenz, E.N. (1963): Deterministic nonperiodic flow. Atmos. Sci. 20, 130CrossRefGoogle Scholar
  24. Rapp, P.E. (1986): Oscillations and chaos in cellular metabolism and physiological systems. In: Chaos. Holden, A.V. (ed.). Manchester, UK: Manchester Univ. Press, pp. 197–202Google Scholar
  25. Röschke, J., Basar E. (1985): Is EEG a simple noise of a “strange attractor”? Pflügers Arch. 405: R45Google Scholar
  26. Röschke, J. (1986): Eine Analyse der nicht-linearan EEG-Dynamik. Dissertation, Universität GöttingenGoogle Scholar
  27. Röschke, J., Basar, E. (1988): The EEG is not a simple noise: Strange attractors in intracranial structures. In: Dynamics of sensory and cognitive processing by the brain. Basgr, E., (ed.). Berlin: Springer, pp. 203–216CrossRefGoogle Scholar
  28. Röschke, J., Basar, E. (1989): Correlation dimensions in various parts of cat and human brain in different states. In: Brain dynamics. Progress and perspectives. Basar, E., Bullock, T.H. (eds.). Berlin: Springer, pp. 131–148CrossRefGoogle Scholar
  29. Saermark, K., Lebech, J., Bak, C.K., Sabers, A. (1989): Magnetoencephalography and attractor dimension. Normal subjects and epileptic patients. In: Brain dynamics. Progress and perspectives. Basgr, E., Bullock, T.H. (eds.). Berlin: Springer, pp. 149–157CrossRefGoogle Scholar
  30. Schutt, A. (1989): The EEG is a quasi-deterministic signal anticipating sensory-cognitive tasks. In: Brain dynamics. Progress and perspectives. Basgr, E., Bullock, T.H. (eds.). Berlin: Springer, pp. 43–71Google Scholar
  31. Skinner, J.E., Martin, J.L., Landisman, C.F., Mommer, M.M., Fulton, K., Mitra, M., Burton, W.D., Saltzberg, B. (1989): Chaotic attractors in a model of neocortex: Dimensionality of olfactory bulb surface potentials are spatially uniform and event-related. In: Brain dynamics. Progress and perspectives. Basar, E., Bullock, T.H. (eds.). Berlin: Springer, pp. 158–173CrossRefGoogle Scholar
  32. Takens, F. (1981): Detecting strange attractors in turbulence. In: Dynamical systems and turbulence. Warwick 1980. Rand, A., Young, L.S., (eds.). Berlin: Springer, pp. 366–381Google Scholar
  33. van Erp, M.G. (1988): On epilepsy: Investigations on the level of the nerve membrane and of the brain. Dissertation, University of Leiden, The NetherlandsGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1990

Authors and Affiliations

  • Erol Başar
  • C. Başar-Eroglu
  • J. Röschke
  • J. Schult

There are no affiliations available

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