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Chaotic Dynamics and Resonance Phenomena in Brain Function: Progress, Perspectives, and Thoughts

  • E. Başar
Chapter

Abstract

My main goal by writing this survey is to try to bridge our knowledge in chaos research with analysis of brain oscillatory phenomena both at the neuronal and the EEG level.

Keywords

Brain Function Chaotic Dynamic Correlation Dimension Strange Attractor Alpha Activity 
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 RH, Shaw CD (1983) Dynamics. The geometry of behaviour, vols 1-3. Aerial, Santa CruzGoogle Scholar
  2. Adey RW (1972) Organization of brain tissue: is the brain a noisy processor? Int J Neurosci 3:271–284PubMedCrossRefGoogle Scholar
  3. Adey RW (1989) Bioinstrumentation — cutting edge and limiting factor in the future of brain research. In: Başar E, Bullock TH (eds) Brain dynamics. Springer, Berlin Heidelberg New York, p 498Google Scholar
  4. Adrian ED (1935) Discharge frequencies in cerebral and cerebellar cortex. J Physiol 83:32–33Google Scholar
  5. Aladjalova NA (1964) Slow electrical processes in the brain. Progress in brain research, vol 7. Elsevier, AmsterdamGoogle Scholar
  6. Albano AM, Mees AI, de Guzman GC, Rapp P (1987) Data requirements for reliable estimation of correlation dimensions. In: Degn H, Holden AV, Olsen LF (eds) Chaos in biological systems. Plenum, New York, pp 207–220Google Scholar
  7. Albano AM, Muench J, Schwartz C, Mees AI, Rapp PE (1988) Singular-value decomposition and the Grassberger-Procaccia algorithm. Am Phys Soc 38(6):3017–3026Google Scholar
  8. Babloyantz A (ed) (1986) Molecules, dynamics, and life. Wiley, New YorkGoogle Scholar
  9. Babloyantz A (1988) Chaotic dynamics in the brain activity. In: Başar E (ed) Dynamics of sensory and cognitive processing of the brain. Springer, Berlin Heidelberg New York, pp 196–202 (Springer series in brain dynamics, vol 1)Google Scholar
  10. Babloyantz A, Destexhe A (1986) Low dimensional chaos in an instance of epilepsy. Proc Natl Acad Sci USA 83:3513PubMedCrossRefGoogle Scholar
  11. 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
  12. Başar E (1976) Biophysical and physiological systems analysis. Addison-Wesley, ReadingGoogle Scholar
  13. Başar E (1980) EEG-brain dynamics. Relation between EEG and brain evoked potentials. El-sevier/North-Holland, AmsterdamGoogle Scholar
  14. Başar E (1983a) 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 183–200Google Scholar
  15. Başar E (1983b) Toward a physical approach to integrative physiology. I. Brain dynamics and physical causality. Am J Physiol 245:R510–R533PubMedGoogle Scholar
  16. Başar E (1988a) Epilogue: brain waves, chaos, learning, and memory. In: Başar E (ed) Dynamics of sensory and cognitive processing by the brain. Springer, Berlin Heidelberg New York, pp 395–406 (Springer series in brain dynamics, vol 1)Google Scholar
  17. Başar E (ed) (1988b) Dynamics of sensory and cognitive processing by the brain. Springer, Berlin Heidelberg New York (Springer series in brain dynamics, vol 1)Google Scholar
  18. Başar E (1988c) 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
  19. Başar E, Bullock TH (eds) (1989) Brain dynamics. Springer, Berlin Heidelberg New York (Springer series in brain dynamics, vol 2)Google Scholar
  20. Başar E, Stampfer HG (1985) Important associations among EEG-dynamics, event-related potentials, short-term memory and learning. Int J Neurosci 26:161–180PubMedCrossRefGoogle Scholar
  21. Başar E, Gönder A, Ungan P (1976) Important relation between EEG and brain evoked potentials. II. A system analysis of electrical signals from the human brain. Biol Cybern 25:41–48PubMedGoogle Scholar
  22. Başar E, Başar-Eroglu C, Röschke J, Schütt A (1984) A new approach to endogenous event-related potentials in man: relation between EEG and P300 wave. Int J Neurosci 24:1–21PubMedCrossRefGoogle Scholar
  23. Başar E, Başar-Eroglu C, Röschke J (1986) Dimensionality of smooth muscle contractions. Conference on perspectives in biological dynamics and theoretical medicine. The New York Academy of Sciences, abstracts book, p 4Google Scholar
  24. Başar E, Başar-Eroglu C, Röschke J (1988) Do coherent patterns of the strange attractor EEG reflect deterministic sensory-cognitive states of the brain. In: Markus M, Müller Sc, Nicolis G (eds) From chemical to biological organization. Springer, Berlin Heidelberg New York, pp 297–306Google Scholar
  25. Başar E, Başar-Eroglu C, Röschke J, Schütt A (1989a) The EEG is a quasi-deterministic signal anticipating sensory-cognitive tasks. In: Başar E, Bullock TH (eds) Brain dynamics. Springer, Berlin Heidelberg New York, pp 43–71 (Springer series in brain dynamics, vol 2)Google Scholar
  26. Basar E, Başar-Eroglu C, Röschke J, Schult J (1989b) Chaos-and alpha-preparation in brain function. In: Cotteril R (ed) Models of brain function. Cambridge University Press pp 365–395Google Scholar
  27. Başar E, Başar-Eroglu C, Röschke J, Schult J (1990) Strange attractor EEG as sign of cognitive function. In: John ER, Harmony T, Prichep L, Valdes-Sosa M, Valdes-Sosa P (eds) Machinery of the mind. Birkhäuser, Boston (in press)Google Scholar
  28. Başar-Eroglu C, Demir N, Tümer N, Türner A, Başar E, Weiss C (1981) Overall myogenic coordination in visceral organs and lymph nodes. In: Başar E, Weiss C (eds) Vasculature and circulation. Elsevier/North-Holland, Amsterdam, pp 227–253Google Scholar
  29. Birkhoff GD (1932) Sur quelques courbes fermées remarquables. Bull Soc Math Fr 60:11–26Google Scholar
  30. Bülbring E, Shuba MF (1976) Physiology of smooth muscle. Raven, New YorkGoogle Scholar
  31. Bullock TH (1976) Redundancy and noise in the nervous system: does the model based on unreliable neurons sell nature short. In: Reuben JP, Purpura DP, Bennett MVL, Kandel ER (eds) Electrobiology of nerve, synapse and muscle. Raven, New YorkGoogle Scholar
  32. Bullock TH (1984) Comparative neuroscience holds promise for quiet revolutions. Science 225:473–478Google Scholar
  33. Bullock TH (1988) Compound potentials of the brain, ongoing and evoked: perspectives from comparative neurology. In: Başar E (ed) Dynamics of sensory and cognitive processing by the brain. Springer, Berlin Heidelberg New York, pp 3–18 (Springer series in brain dynamics, vol 1)CrossRefGoogle Scholar
  34. Bullock TH (1989a) The micro-EEG represents varied degrees of cooperativity among wideband generators. In: Başar E, Bullock TH (eds) Brain dynamics. Springer, Berlin Heidelberg New York, pp 5–12 (Springer series in brain dynamics, vol 2)Google Scholar
  35. Bullock TH (1989b) Epilogue: signs of dynamic processes in organized neural tissue: extracting order from chaotic data. In: Başar E, Bullock TH (eds) Brain dynamics. Springer, Berlin Heidelberg New York, pp 539–547 (Springer series in brain dynamics, vol 2)Google Scholar
  36. Bullock TH, Başar E (1988) Comparison of ongoing compound field potentials in the brains of invertebrates and vertebrates. Brain Res Rev 13:57–75CrossRefGoogle Scholar
  37. Dvorak I, Siska J (1986) On some problems encountered in the estimation of the correlation dimension of the EEG. Phys Lett A 118:63–66CrossRefGoogle Scholar
  38. Eckhorn R, Bauer R, Jordan W, Brosch M, Kruse W, Munk M, Reitboeck HJ (1988) Coherent oscillations: a mechanism of feature linking in the visual cortex? Biol Cybern 60:121–130PubMedCrossRefGoogle Scholar
  39. Eckhorn R, Reitboeck HJ, Arndt M, Dicke P (1989a) Feature linking via stimulus — evoked oscillations: experimental results from cat visual cortex and functional implications from a network model. Conference on Neural Networks, Washington, abstract volumeGoogle Scholar
  40. Eckhorn R, Bauer R, Reitboeck HJ (1989b) Discontinuities in visual cortex and possible functional implications: relating cortical structure and function with multielectrode/correlation techniques. In: Başar E, Bullock TH (eds) Brain dynamics. Springer, Berlin Heidelberg New York, pp 267–278 (Springer series in brain dynamics, vol 2)Google Scholar
  41. Freeman WJ (ed) (1975) Mass action in the nervous system. Academic, New YorkGoogle Scholar
  42. Freeman WJ (1979) Nonlinear gain mediating cortical stimulus response relations. Biol Cybern 33:237–247PubMedCrossRefGoogle Scholar
  43. Freeman WJ (1983) Dynamics of image formation by nerve cell assemblies. In: Başar E, Flohr H, Haken H, Mandell AJ (eds) Synergetics of the brain. Springer, Berlin Heidelberg New York, pp 102–121Google Scholar
  44. Freeman WJ (1989) Analysis of strange attractors in EEGs with kinesthetic experience and 4-D computer graphics. In: Başar E, Bullock TH (eds) Brain dynamics. Springer, Berlin Heidelberg New York, pp 512–520 (Springer series in brain dynamics, vol 2)Google Scholar
  45. Freeman W, Skarda CA (1985) Spatial EEG-patterns, non-linear dynamics and perception: the neo-Sherringtonian view. Brain Res Rev 10:147–175CrossRefGoogle Scholar
  46. Galambos R, Makeig S, Talmachoff PJ (1981) A 40-Hz auditory potential recorded from the human scalp. Proc Natl Acad Sci USA 78:2643–2647PubMedCrossRefGoogle Scholar
  47. Gebber GL (1980) Central oscillators responsible for sympathetic nerve discharge. Am J Physiol 239:H143–H155PubMedGoogle Scholar
  48. Gebber GL, Barman SM (1980) Basis for 2-6 cycle/s rhythm in sympathetic nerve discharge. Am J Physiol 239:R48–R56PubMedGoogle Scholar
  49. Gebber GL, Barman SM (1981) Sympathetic-related activity of brain stem neurons in baroreceptor-denervated cats. Am J Physiol 240:R348–R355PubMedGoogle Scholar
  50. Gebber GL, McCall RB (1976) Identification and discharge patterns of spinal sympathetic inter-neurons. Am J Physiol 231:722–733PubMedGoogle Scholar
  51. Gleick J (1987) Chaos: making a new science. Penguin, New YorkGoogle Scholar
  52. Golenhofen K (1970) Slow rhythms in smooth muscle (minute rhythm). In: Bülbring E, Shuba MF (eds) Smooth muscle. Arnold, LondonGoogle Scholar
  53. Gönder A, Başar E (1978) Evoked frequency stabilization in the electric activity of the cat brain. Biol Cybern 31:193–204PubMedCrossRefGoogle Scholar
  54. Graf KE, Elbert T (1989) Dimensional analysis of the waking EEG. In: Başar E, Bullock TH (eds) Brain dynamics. Springer, Berlin Heidelberg New York, pp 174–191 (Springer series in brain dynamics, vol 2)Google Scholar
  55. Grassberger P, Procaccia I (1983) Measuring the strangeness of strange attractors. Physica (D)9:183–208Google Scholar
  56. Gray CM, Singer W (1987) Stimulus specific neuronal oscillations in the cat visual cortex: a cortical function unit. Soc Neurosci 404:3Google Scholar
  57. Gray CM, Singer W (1989) Stimulus-specific neuronal oscillations in orientation columns of cat visual cortex. Proc Natl Acad Sci USA 86:1698–1702PubMedCrossRefGoogle Scholar
  58. Gray CM, König P, Engel AK, Singer W (1989) Oscillatory response in cat visual cortex exhibit inter-columnar synchronization which reflects global stimulus properties. Nature 338:334–337PubMedCrossRefGoogle Scholar
  59. Haken H (1976) Synergetics. An introduction. Springer, Berlin Heidelberg New YorkGoogle Scholar
  60. Haken H (ed) (1983) Advanced synergetics. Springer, Berlin Heidelberg New YorkGoogle Scholar
  61. Kaiser F (1988) Theory of non-linear excitations. In: Fröhlich H (ed) Biological coherence and response to external stimuli. Springer, Berlin Heidelberg New YorkGoogle Scholar
  62. Keidel M, Keidel WD, Tirsch WS, Pöppl SJ (1987) Studying temporal order in human CNS by means of “running” frequency and coherence analysis. In: Rensing L, an der Heiden U, Mackey MC (eds) Temporal disorder in human oscillatory systems. Springer, Berlin Heidelberg New York (Springer series in synergetics, vol 36)Google Scholar
  63. Keidel M, Keidel WD, Tirsch WS, Pöppl SJ (1989) Temporal pattern with circa 1 minute cycles in the running coherence function between EEG and VMG in man. (In press)Google Scholar
  64. Layne SP, Mayer-Kress G, Holzfuss J (1986) Problems associated with dimensional analysis of electroencephalogram data. In: Mayer-Kress G (ed) Dimensions and entropies in chaotic systems. Springer, Berlin Heidelberg New York, p 246CrossRefGoogle Scholar
  65. Llinâs RR (1988) The intrinsic electrophysiological properties of mammalian neurons: insights into central nervous system function. Science 242:1654–1664PubMedCrossRefGoogle Scholar
  66. Lopes da Silva FH, Van Rotterdam A, Barts P. Van Heusden E, Barr W (1976) Models of neuronal populations: the basic mechanisms of rhythmicity. Prog Brain Res 45:281–308CrossRefGoogle Scholar
  67. Lopes da Silva FH, Kamphuis W, van Neerven JMAM, Pijn JPM (1990) Cellular and network mechanisms in the kindling model of epilepsy: the role of GABAergic inhibition and the emerge of strange attractors. In: John ER, Harmony T, Prichep L, Valdes-Sosa M, Valdes-Sosa P (eds) Machinery of the mind. Birkhäuser, BostonGoogle Scholar
  68. Mees AI, Rapp PE, Jennings LS (1987) Singular-value decomposition and embedding dimension. Physiol Rev A 36:340–346CrossRefGoogle Scholar
  69. Mpitsos GJ (1989) Chaos in brain function and the problem of nonstationarity: a commentary. In: Başar E, Bullock TH (eds) Brain dynamics. Springer, Berlin Heidelberg New York, pp 521–535 (Springer series in brain dynamics, vol 2)Google Scholar
  70. Pfurtscheller G, Steffan J, Maresch H (1988) ERD mapping and functional topography: temporal and spatial aspects. In: Pfurtscheller G, Lopes da Silva FH (eds) Functional brain imaging. Huber, Toronto, pp 117–130Google Scholar
  71. Poincaré H (1892) Les méthodes nouvelles de la mécanique céleste. Gauthier-Villars, ParisGoogle Scholar
  72. Pool R (1989) Is it healthy to be chaotic? Science 243:604–605PubMedCrossRefGoogle Scholar
  73. Rapp PE, Zimmermann ID, Albano AM, Deguzman GC, Greenbaum NN (1985a) Dynamics of spontaneous neural activity in the simian motor cortex: the dimension of chaotic neurons. Phys Lett (A) 110:335–338CrossRefGoogle Scholar
  74. Rapp PE, Zimmermann ID, Albano AM, de Guzman GC, Greenbaum NN, Bashore TR (1985b) Experimental studies of chaotic neural behaviour: cellular activity and electroen-cephalographic signals. In: Othmer HG (ed) Nonlinear oscillations in biology and chemistry. Springer, Berlin Heidelberg New York, pp 175–205Google Scholar
  75. Rapp PE, Albano AM, Guzman GC, Greenbaum NN, Bashore TR (1986) In: Othmer HG (ed) Nonlinear oscillations in biology and chemistry. Springer, Berlin Heidelberg New York, p 175 (Lecture notes in biomathematics, vol 66)Google Scholar
  76. Rapp PE, Bashore TR, Martinerie JM, Albano AM, Mees AI (1989) Dynamics of brain electrical activity. Brain Topography (in press)Google Scholar
  77. Röschke J (1986) Eine Analyse der nichtlinearen EEG-Dynamik. Doctoral dissertation, University of GöttingenGoogle Scholar
  78. Röschke J, Başar E (1985) Is EEG a simple noise or a “strange attractor”? Pflügers Arch 405:R45Google Scholar
  79. 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
  80. Röschke J, Başar E (1989) Correlation dimensions in various parts of cat and human brain in different states. In: Başar E, Bullock TH (eds) Brain dynamics. Springer, Berlin Heidelberg New York, pp 131–148 (Springer series in brain dynamics, vol 2)Google Scholar
  81. Rosen R (1969) Hierarchical organization in automata theoretic models of the central nervous system: In: Leibovic KN (ed) Information processing in the nervous system. Springer, Berlin Heidelberg New YorkGoogle Scholar
  82. Rössler OE, Hudson JL (1989) Self-similarity in hyperchaotic data. In: Başar E, Bullock TH (eds) Brain dynamics. Springer, Berlin Heidelberg New York, pp 113–121 (Springer series in brain dynamics, vol 2)Google Scholar
  83. Saermark K, Lebech J, Bak CK, Sabers A (1989) Magnetoencephalography and attractor dimension: normal subjects and epileptic patients. In: Başar E, Bullock TH (eds) Brain dynamics. Springer, Berlin Heidelberg New York, pp 149–157 (Springer series in brain dynamics, vol 2)Google Scholar
  84. Schuster HG (1988) Deterministic chaos. VCH, WeinheimGoogle Scholar
  85. Skarda CA, Freeman WJ (1987) How brains make chaos in order to make sense of the world. Behav Brain Sci 10:161–195CrossRefGoogle Scholar
  86. Skinner JE, Reed JC (1981) Blockade of a frontocortical-brainstem pathway prevents ventricular fibrillation of the ischemic heart in pigs. Am J Physiol 240:H1156–H1163Google Scholar
  87. Skinner JE, Martin JL, Landisman CE, Mommer MM, Fulton K, Mitra M, Burton WD, Saltzberg B (1989) Chaotic attractors in a model of neocortex: dimensionalitites of olfactory bulb surface potentials are spatially uniform and event related. In: Başar E, Bullock TH (eds) Brain dynamics. Springer, Berlin Heidelberg New York, pp 158–173 (Springer series in brain dynamics, vol 2)Google Scholar
  88. Storm Van Leeuwen W (1977) The alpha rhythm. In: Cobb WA, van Duijn H (eds) Contemporary clinical neurophysiology. Electroencephalogr Clin Neurophysiol Suppl 34:1–7Google Scholar
  89. Stryker MP (1989) Is grandmother an oscillation? Nature 338:297–298Google Scholar
  90. Van Erp MG (1988) On epilepsy: investigations on the level of the nerve membrane and of the brain. Proefschrift Rijksuniversiteit, LeidenGoogle Scholar
  91. Walter WG (1964) The convergence and interaction of visual, auditory, and tactile responses in human nonspecific cortex. Ann NY Acad Sci 112:320–361PubMedCrossRefGoogle Scholar

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