Advertisement

Correlation Dimensions in Various Parts of Cat and Human Brain in Different States

  • J. Röschke
  • E. Başar

Abstract

The analysis of deterministic chaos is currently an active field in many branches of research. Mathematically, all nonlinear dynamical systems with more than two degrees of freedom can generate chaos and, therefore, become unpredictable over a longer time scale. In order to describe periodic, aperiodic, or even chaotic behavior of nonlinear systems, several approaches have been used. In 1963 Lorenz applied concepts of nonlinear dynamics to the convection phenomenon in hydrodynamics in order to describe atmospheric turbulence (Navier-Stokes equation). He demonstrated the possibility that the unpredictable or chaotic behavior observed in an infinite-dimensional system might be caused by a three-dimensional dynamical system. Our research group’s first nonlinear approach consisted in comparing the relation between EEG and evoked potentials by considering the Duffing equation as an adequate nonlinear model (Başar 1980). Later, assuming the EEG to be a chaotic attractor and mentioning the possibilities of applying the Navier-Stokes equation for comparison, we described that the EEG might reflect properties of a strange attractor (Başar 1983; Başar and Röschke 1983).

Keywords

Auditory Cortex Cerebellar Cortex Correlation Dimension Inferior Colliculus Strange Attractor 
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. Abraham RH, Shaw CD (1983) Dynamics — the geometry of behavior. Part 2: chaotic behavior. Aerial Press, Santa CruzGoogle Scholar
  2. Adrian ED (1935) Discharge frequencies in cerebral and cerebellar cortex. J Physiol 83:32–33Google Scholar
  3. Babloyantz A (1988) Chaotic dynamics in brain activity. In: Başar E (ed) Dynamics of sensory and cognitive processing by the brain. Springer, Berlin Heidelberg New York, pp 196–202 (Springer series in brain dynamics, vol 1)CrossRefGoogle Scholar
  4. Babloyantz A, Nicolis C, Salazar M (1985) Evidence of chaotic dynamics. Phys Lett[A]:152–156Google Scholar
  5. Başar E (1972) Remarks on mathematical signal processing by the brain during rhythmic neuro-physiological stimulation. Int J Neurosci 4:71–76CrossRefGoogle Scholar
  6. Başar E (1980) EEG-brain dynamics. Relation between EEG and brain evoked potentials. El-sevier/North-Holland, AmsterdamGoogle Scholar
  7. Başar E (1983) Toward a physical approach to integrative physiology. I. Brain dynamics and physical causality. Am J Physiol 245(4):R510–R533PubMedGoogle Scholar
  8. Başar E (1988) EEG-dynamics and evoked potentials in sensory and cognitive processing by the brain. In: Başar E (ed) Dynamics of sensory and cognitive processing by the brain. Springer, Berlin Heidelberg New York, pp 30–55 (Springer series in brain dynamics, vol 1)Google Scholar
  9. Başar E, Röschke J (1983) Synergetics of neuronal populations. A survey on experiments. In: Başar E, Flohr H, Haken H, Mandell AJ (eds) Synergetics of the brain. Springer, Berlin Heidelberg New York, pp 199–200 (Springer series in synergetics, vol 23)Google Scholar
  10. Başar E, Demir N, Gönder A, Ungan P (1979) Combined dynamics of EEG and evoked potentials. I. Studies of simultaneously recorded EEG-EPograms in the auditory pathway, retic-ular formation and hippocampus of the cat brain during the waking stage. Biol Cybern 34:1–19PubMedCrossRefGoogle Scholar
  11. Başar E, Rosen B, Başar-Eroglu C, Greitschus F (1987) The associations between 40 Hz-EEG and the middle latency response of the auditory evoked potentials. Int J Neurosci 33:103–117PubMedCrossRefGoogle Scholar
  12. Başar E, Başar-Eroglu C, Röschke J (1988) Do coherent patterns of the strange attractor EEG reflect sensory-cognitive states of the brain? In: Markus M, Müller S, Nicolis G (eds) From chemical to biological organization. Springer, Berlin Heidelberg New YorkGoogle Scholar
  13. Freeman WJ (1988) Nonlinear neural dynamics in olfaction as a model for cognition. In: Başar E (ed) Dynamics of sensory and cognitive processing by the brain. Springer, Berlin Heidelberg New York, pp 19–29 (Springer series in brain dynamics, vol 1)CrossRefGoogle Scholar
  14. Grassberger P, Procaccia I (1983) Measuring the strangeness of strange attractors. Physica [D]9:183–208Google Scholar
  15. Lorenz EN (1963) Deterministic nonperiodic flow. Atmos Sci 20:130CrossRefGoogle Scholar
  16. Röschke J (1986) Eine Analyse der nichtlinearen EEG-Dynamik. Doctoral dissertation, University of GöttingenGoogle Scholar
  17. Röschke J, Başar E (1985a) A phase portrait analysis of the EEG and evoked potentials. Elec-troencephalogr Clin Neurophysiol 61:S114CrossRefGoogle Scholar
  18. Röschke J, Başar E (1985b) Is EEG a simple noise or a “strange attractor”? Pflugers Arch 405(2):R45Google Scholar
  19. Röschke J, Başar E (1988) The EEG is not a simple noise. Strange attractors in intracranial structures. In: Başar E (ed) Dynamics of sensory and cognitive processing by the brain. Springer, Berlin Heidelberg New York, pp 203–216 (Springer series in brain dynamics, vol 1)CrossRefGoogle Scholar
  20. Schroeder MR (1986) Number theory in science and communication. Springer, Berlin Heidelberg New YorkGoogle Scholar
  21. Schuster HG (1984) Determnistic chaos. An introduction. Physik, WeinheimGoogle Scholar
  22. Takens F (1981) Detecting strange attractants in turbulence. In: Rand DA, Young LS (eds) Dynamical systems and turbulence, Warwick 1980. Springer, Berlin Heidelberg New York, pp 366–381 (Lecture notes in mathematics, vol 898)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1990

Authors and Affiliations

  • J. Röschke
  • E. Başar

There are no affiliations available

Personalised recommendations