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.
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References
Abraham, R.H., Shaw, C.D. (1983): Dynamics. The geometry of behavior. Santa Cruz, CA: Ariel Press
Babloyantz, A. (1988): Chaotic dynamics in brain activity. In: Dynamics of sensory and cognitive processing by the brain. Basar, E. (ed.). Berlin: Springer, pp. 196–202
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. 122–130
Babloyantz, A., Nicolis, C., Salazar, M. (1985): Evidence of chaotic dynamics of brain activity during the sleep cycle. Phys. Lett. [A] 111, 152–156
Basşr, E. (1980): EEG-brain dynamics. Relation between EEG and brain evoked potentials. Amsterdam: Elsevier/North-Holland
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. 183–200
Başar, E. (1983b): Toward a physical approach to integrative physiology. I: Brain dynamics and physical causality. Am. J. Physiol. 245, R510 — R533
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. 30–55
Başar, E., Bullock, T.H. (1989): Brain dynamics. Progress and perspectives. Berlin: Springer
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. 199–200
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, 1–21
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. 297–306
Berger, H. (1938): Das Elektroencephalogramm des Menschen. Nova Acta Leopold. 6, 38
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.
Bullock, T.H. (eds.). Berlin: Springer, pp. 537–547
Dvorak, I., Siska, J. (1986): On some problems encountered in the estimation of the correlation dimension of the EEG. Phys. Lett. A 118, 63–66
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. 102–121
Freeman, W.J., Skarda, C.A. (1985): Spatial EEG patterns, non-linear dynamics and perception: The neo-Sherringtonian view. Brain Res. Rev. 10, 147–175
Grassberger, P., Procaccia, I. (1983): Measuring the strangeness of strange attractors. Physica [D] 9, 183–208
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, 1–52
Kornhuber, H.H., Deecke, L. (1965): Hirnpotentialänderungen bei Willkürbewegungen and passiven Bewegungen des Menschen: Bereitschaftspotential and reafferente Potentiale. Pflügers. Arch. 284, 1–17
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. 246
Lorenz, E.N. (1963): Deterministic nonperiodic flow. Atmos. Sci. 20, 130
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. 197–202
Röschke, J., Basar E. (1985): Is EEG a simple noise of a “strange attractor”? Pflügers Arch. 405: R45
Röschke, J. (1986): Eine Analyse der nicht-linearan EEG-Dynamik. Dissertation, Universität Göttingen
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. 203–216
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. 131–148
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. 149–157
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. 43–71
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. 158–173
Takens, F. (1981): Detecting strange attractors in turbulence. In: Dynamical systems and turbulence. Warwick 1980. Rand, A., Young, L.S., (eds.). Berlin: Springer, pp. 366–381
van Erp, M.G. (1988): On epilepsy: Investigations on the level of the nerve membrane and of the brain. Dissertation, University of Leiden, The Netherlands
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Başar, E., Başar-Eroglu, C., Röschke, J., Schult, J. (1990). Strange Attractor EEG as Sign of Cognitive Function. In: John, E.R., Harmony, T., Prichep, L.S., Valdés-Sosa, M., Valdés-Sosa, P.A. (eds) Machinery of the Mind. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4757-1083-0_5
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