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.
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References
Abraham RH, Shaw CD (1983) Dynamics. The geometry of behaviour, vols 1-3. Aerial, Santa Cruz
Adey RW (1972) Organization of brain tissue: is the brain a noisy processor? Int J Neurosci 3:271–284
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 498
Adrian ED (1935) Discharge frequencies in cerebral and cerebellar cortex. J Physiol 83:32–33
Aladjalova NA (1964) Slow electrical processes in the brain. Progress in brain research, vol 7. Elsevier, Amsterdam
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 207–220
Albano AM, Muench J, Schwartz C, Mees AI, Rapp PE (1988) Singular-value decomposition and the Grassberger-Procaccia algorithm. Am Phys Soc 38(6):3017–3026
Babloyantz A (ed) (1986) Molecules, dynamics, and life. Wiley, New York
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)
Babloyantz A, Destexhe A (1986) Low dimensional chaos in an instance of epilepsy. Proc Natl Acad Sci USA 83:3513
Babloyantz A, Nicolis C, Salazar M (1985) Evidence of chaotic dynamics of brain activity during the sleep cycle. Phys Lett (A) 111:152–156
Başar E (1976) Biophysical and physiological systems analysis. Addison-Wesley, Reading
Başar E (1980) EEG-brain dynamics. Relation between EEG and brain evoked potentials. El-sevier/North-Holland, Amsterdam
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 183–200
Başar E (1983b) Toward a physical approach to integrative physiology. I. Brain dynamics and physical causality. Am J Physiol 245:R510–R533
Başar E (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)
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)
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)
Başar E, Bullock TH (eds) (1989) Brain dynamics. Springer, Berlin Heidelberg New York (Springer series in brain dynamics, vol 2)
Başar E, Stampfer HG (1985) Important associations among EEG-dynamics, event-related potentials, short-term memory and learning. Int J Neurosci 26:161–180
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 25:41–48
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 24:1–21
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 4
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 297–306
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)
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 365–395
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)
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 227–253
Birkhoff GD (1932) Sur quelques courbes fermées remarquables. Bull Soc Math Fr 60:11–26
Bülbring E, Shuba MF (1976) Physiology of smooth muscle. Raven, New York
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 York
Bullock TH (1984) Comparative neuroscience holds promise for quiet revolutions. Science 225:473–478
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)
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)
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)
Bullock TH, Başar E (1988) Comparison of ongoing compound field potentials in the brains of invertebrates and vertebrates. Brain Res Rev 13:57–75
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
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 60:121–130
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 volume
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)
Freeman WJ (ed) (1975) Mass action in the nervous system. Academic, New York
Freeman WJ (1979) Nonlinear gain mediating cortical stimulus response relations. Biol Cybern 33:237–247
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 102–121
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)
Freeman W, Skarda CA (1985) Spatial EEG-patterns, non-linear dynamics and perception: the neo-Sherringtonian view. Brain Res Rev 10:147–175
Galambos R, Makeig S, Talmachoff PJ (1981) A 40-Hz auditory potential recorded from the human scalp. Proc Natl Acad Sci USA 78:2643–2647
Gebber GL (1980) Central oscillators responsible for sympathetic nerve discharge. Am J Physiol 239:H143–H155
Gebber GL, Barman SM (1980) Basis for 2-6 cycle/s rhythm in sympathetic nerve discharge. Am J Physiol 239:R48–R56
Gebber GL, Barman SM (1981) Sympathetic-related activity of brain stem neurons in baroreceptor-denervated cats. Am J Physiol 240:R348–R355
Gebber GL, McCall RB (1976) Identification and discharge patterns of spinal sympathetic inter-neurons. Am J Physiol 231:722–733
Gleick J (1987) Chaos: making a new science. Penguin, New York
Golenhofen K (1970) Slow rhythms in smooth muscle (minute rhythm). In: Bülbring E, Shuba MF (eds) Smooth muscle. Arnold, London
Gönder A, Başar E (1978) Evoked frequency stabilization in the electric activity of the cat brain. Biol Cybern 31:193–204
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)
Grassberger P, Procaccia I (1983) Measuring the strangeness of strange attractors. Physica (D)9:183–208
Gray CM, Singer W (1987) Stimulus specific neuronal oscillations in the cat visual cortex: a cortical function unit. Soc Neurosci 404:3
Gray CM, Singer W (1989) Stimulus-specific neuronal oscillations in orientation columns of cat visual cortex. Proc Natl Acad Sci USA 86:1698–1702
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 338:334–337
Haken H (1976) Synergetics. An introduction. Springer, Berlin Heidelberg New York
Haken H (ed) (1983) Advanced synergetics. Springer, Berlin Heidelberg New York
Kaiser F (1988) Theory of non-linear excitations. In: Fröhlich H (ed) Biological coherence and response to external stimuli. Springer, Berlin Heidelberg New York
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)
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)
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 246
Llinâs RR (1988) The intrinsic electrophysiological properties of mammalian neurons: insights into central nervous system function. Science 242:1654–1664
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 45:281–308
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, Boston
Mees AI, Rapp PE, Jennings LS (1987) Singular-value decomposition and embedding dimension. Physiol Rev A 36:340–346
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)
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 117–130
Poincaré H (1892) Les méthodes nouvelles de la mécanique céleste. Gauthier-Villars, Paris
Pool R (1989) Is it healthy to be chaotic? Science 243:604–605
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) 110:335–338
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 175–205
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)
Rapp PE, Bashore TR, Martinerie JM, Albano AM, Mees AI (1989) Dynamics of brain electrical activity. Brain Topography (in press)
Röschke J (1986) Eine Analyse der nichtlinearen EEG-Dynamik. Doctoral dissertation, University of Göttingen
Röschke J, Başar E (1985) Is EEG a simple noise or a “strange attractor”? Pflügers Arch 405:R45
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)
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)
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 York
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)
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)
Schuster HG (1988) Deterministic chaos. VCH, Weinheim
Skarda CA, Freeman WJ (1987) How brains make chaos in order to make sense of the world. Behav Brain Sci 10:161–195
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–H1163
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)
Storm Van Leeuwen W (1977) The alpha rhythm. In: Cobb WA, van Duijn H (eds) Contemporary clinical neurophysiology. Electroencephalogr Clin Neurophysiol Suppl 34:1–7
Stryker MP (1989) Is grandmother an oscillation? Nature 338:297–298
Van Erp MG (1988) On epilepsy: investigations on the level of the nerve membrane and of the brain. Proefschrift Rijksuniversiteit, Leiden
Walter WG (1964) The convergence and interaction of visual, auditory, and tactile responses in human nonspecific cortex. Ann NY Acad Sci 112:320–361
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Başar, E. (1990). Chaotic Dynamics and Resonance Phenomena in Brain Function: Progress, Perspectives, and Thoughts. In: Başar, E. (eds) Chaos in Brain Function. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-75545-3_1
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