Skip to main content
    • Aa
    • Aa

Dynamics of the brain at global and microscopic scales: Neural networks and the EEG

  • J. J. Wright (a1) (a2) and D. T. J. Liley (a1) (a2)

There is some complementarity of models for the origin of the electroencephalogram (EEG) and neural network models for information storage in brainlike systems. From the EEG models of Freeman, of Nunez, and of the authors' group we argue that the wavelike processes revealed in the EEG exhibit linear and near-equilibrium dynamics at macroscopic scale, despite extremely nonlinear – probably chaotic – dynamics at microscopic scale. Simulations of cortical neuronal interactions at global and microscopic scales are then presented. The simulations depend on anatomical and physiological estimates of synaptic densities, coupling symmetries, synaptic gain, dendritic time constants, and axonal delays. It is shown that the frequency content, wave velocities, frequency/wavenumber spectra and response to cortical activation of the electrocorticogram (ECoG) can be reproduced by a “lumped” simulation treating small cortical areas as single-function units. The corresponding cellular neural network simulation has properties that include those of attractor neural networks proposed by Amit and by Parisi. Within the simulations at both scales, sharp transitions occur between low and high cell firing rates. These transitions may form a basis for neural interactions across scale. To maintain overall cortical dynamics in the normal low firing-rate range, interactions between the cortex and the subcortical systems are required to prevent runaway global excitation. Thus, the interaction of cortex and subcortex via corticostriatal and related pathways may partly regulate global dynamics by a principle analogous to adiabatic control of artificial neural networks.

Hide All
H. D. I. Abarbanel , R. Brown , J. J. Sidorowich & L. S. Tsimring (1993) The analysis of observed chaotic data in physical systems. Review of Modem Physics 65: 1331–92. [LI]

M. Abeles (1982) Local cortical circuits. In: Studies in brain Junction 6. Springer-Verlag. [RM]

M. Abeles , Y. Prut , H. Bergman & E. Vaadia (1994) Synchronization in neuronal transmission and its importance for information processing. In: Temporal coding in the brain, ed. G. Buzsaki , R. Llinas , W. Singer , A. Berthoz & Cristen . Springer-Verlag. [ZJK]

A. Aertsen & M. Amdt (1993) Response synchronization in the visual cortex. Current Opinion in Neurobiology 3:586–94. [HP]

D. Alkon , J.-V Sanchez-Andres , E. Ito & K. Oka (1992) Long-term transformation of an inhibitory into an excitatory GABAergic synaptic response. Proceedings of the National Academy of Sciences 89(24):11862–66. [HRE]

D. J. Amit (1995) The Hebbian paradigm reintegrated. Behavioral and Brain Sciences 18:681. [DJA]

D. J. Amit & M. V. Tsodyks (1990) Attractor neural networks with biological probe records. Network 1:381405. [aJJW]

D. J. Amit & M. V. Tsodyks (1991) Quantitative study of attractor neural networks retrieving at low spike rates: 2. Low rate retrieval in symmetric networks. Network 2:275–94. [ajJW]

I. Aradi , G. Barna , P. Érdi & T. Gröbler (1995) Chaos and learning in the olfactory bulb. International Journal of Intelligent Systems 10:89117. [PÉ]

A. Babloyantz & C. Lourenco (1994) Computation with chaos: A paradign for cortical activity. Proceedings of the National Academy of Sciences USA 91:9027–31. [IT]

C. J. Becker & W. J. Freeman (1968) Prepyriform electrical activity after loss of peripheral or central input or both. Physiology & Behavior 3:597–99. [WJF]

C. H. Bennett 91995) Quantum information and computation. Physics Today 48:2430. [LI]

J. M. Bower & D. Beeman (1995) The book of Genesis: Exploring realistic neural models with GEneral NEural SImulation System. TELOS/Springer-Verlag. [JJW]

V. Braitenberg & A. Schuz (1991) Anatomy of the cortex: Statistics and geometry. Springer-Verlag. [aJJW]

S. L. Bressler , R. Coppola & R. Nakamura (1993) Episodic multiregional cortical coherence at multiple frequencies during visual task performance. Nature 366:153–56. [HRE, rJJW]

S. L. Bressler & W. J. Freeman (1980) Frequency analysis of olfactory system EEC in cat, rabbit and rat. EEC and Clinical Neurophysiology 50:1924. [WJF]

T. H. Bullock & M. C. McClune (1989) Lateral coherence of the electrocorticogram: A new measure of brain synchrony. Electroencephalography and Clinical Neurophysiology 73:479–98. [THB]

T. H. Bullock , M. C McClune , J. Z. Achimowicz , V. J. Iragui-Madoz , R. B. Duckrow & S. S. Spencer (1995) EEC coherence has structure in the millimeter domain: Subdural and hippocampal recordings from epileptic patients. Electroencephalography and Clinical Neurophysiology 95:161–77. [THB]

B. Buzsaki & J. J. Chrobak (1995) Temporal structure in spatially organized neuronal emsembles: A role for intemeuronal networks. Current Opinion in Neurobiology 5:504–20. [EK]

E. R. Caianiello , A. De Luca & L. M. Ricciardi (1967) Reverberations and control of neural networks. Kybernetik 4:1018. [aJJW]

R. Case (1992) The role of the frontal lobes in the regulation of cognitive development. Brain and Cognition 20:5173. [AO]

S. Dehaene , J. P. Changeux & J. P. Nadal (1987) Neural networks that learn temporal sequences by selection. Proceedings of the National Academy of Science 84:2727–31. [aJJW]

B. S. DeWitt (1957) Dynamical theory in curved spaces: 1. A review of the classical and quantum action principles. Review of Modem Physics 29:377–97. [LI]

E. Donchin (1981) Suprise! … Surprise? Psychophysiology 18:493513. [MM]

F. H. Eeckman & W. J. Freeman (1991) Asymmetric sigmoid nonlinearity in the rat olfactory system. Brain Research 557:1321. [aJJW]

P. Érdi (1983) Hierarchical approach to the brain. International Journal of Neuroscience 20:193216. [PÉ]

W. J. Freeman (1964) A linear distributed feedback model for prepyriform cortex. Experimental Neurology 10:525–47. [aJJW]

W. J. Freeman (1975) Mass action in the nervous system. Academic Press. [aJJW, HRE, WJF, PLN]

W. J. Freeman (1979) Nonlinear gain mediation of cortical stimulus response relations. Biological Cybernetics 33:237–47. [aJJW, WJF, HL]

W. J. Freeman (1987b) Simulation of chaotic EEC patterns with dynamic model of the olfactory system. Biological Cybernetics 56:139–50. [aJJW]

W. J. Freeman (1988) Strange attractors diat govern mammalian brain dynamics shown by trajectories of electroencephalographic (EEG) potential. IEEE Transactions on Circuits and Systems 35:781–83. [aJJW]

W. J. Freeman (1992) Tutorial in neurobiology: From single neurons to brain chaos. International Journal of Bifurcation and Chaos 2:451–82. [WJF]

W. J. Freeman (1994) Neural mechanisms underlying destabilization of cortex by sensory input. Physica D 75:151–64. [IT]

W. J. Freeman (1995c) Chaos in the brain: Possible roles in biological intelligence. International Journal of Intelligent Systems 10:7188. [IT]

W. J. Freeman & J. M. Barrie (1994) Chaotic oscillations and the genesis of meaning in cerebral cortex. In: Temporal coding in the brain, ed. C. Buzsaki , R. Llinás , W. Singer , A. Berthoz & Y. Christen . Springer-Verlag. [WJF]

W. J. Freeman & C. A. Skarda (1985)' Spatial EEG patterns, nonlinear dynamics and perception: The neo-Sherringtonian view. Brain Research Reviews 10:147–75. [aJJW]

R. Friedrich , A. Fuchs & H. Hakan (1991) Spatio-temporal EEG patterns. In: Rhythms in physiological systems, ed. H. Hakan & H. P. Koepshen . Springer-Verlag. [PLN]

A. Fuchs , J. A. S. Kelso & H. Hakan (1992) Phase transitions in the human brain spatial mode dynamics. International Journal of Bifurcation and Chaos 2:917–39. [PLN]

A. S. Gevins , R. E. Schaffer , J. C. Doyle , B. A. Cuttilo , R. S. Tannehill & S. L. Bressler (1983) Shadows of thought: Shifting lateralisation of human brain electrical patterns during a brief visuomotor task. Science 220:9799. [aJJW]

R. Graham (1978) Path-integral methods on nonequilibrium thermodynamics and statistics. In: Stochastic processes in nonequilibrium systems, ed. L. Garrido , P. Seglar & P. J. Shepherd . Springer-Verlag. [LI]

P. Grassberger & I. Procaccia (1983) Measuring die strangeness of strange attractors. Physica D 9:189208. [MM, WSP]

C. M. Gray , P. Koenig , K. A. Engel & W. Singer (1989) Oscillatory responses in cat visual cortex exhibit intereolumnar synchronisation which reflects global stimulus properties. Nature 338:334–37. [aJJW, HP]

R. A. M. Gregson (1992) Cognitive load as a determinant of the dimensionality of the electroencephalogram: A replication study. Biological Psychology 35:165–78. [MM]

M. Griniasty , M. V. Tsodyks & D. J. Amit (1993) Conversion of temporal correlations between stimuli to spatial correlations between attractors. Neural Computation 5:117. [aJJW]

H. Haken (1977) Synergistics: An introduction. Springer-Verlag. [PÈ]

J. J. Hopfield (1982) Neural networks and physical systems with emergent collective computational abilities. Proceedings of National Academy of Sciences 79:2554–58. [aJJW]

J. J. Hopfield (1984) Neurones with graded response have collective computational properties like those of two state neurones. Proceedings of National Academy of Science 81:3088–92. [aJJW]

J. J. Hopfield & D. W. Tank (1986) Computing with neural circuits: A model. Science 233:625–33. [aJJW]

K. Ikeda , K. Otsuka & K. Matsumoto (1989) Maxwell-Bloch turbulence. Progress of Theoretical Physics [Suppl.] 99:295313. [IT]

L. Ingber (1981) Towards a unified brain theory. Journal of Social and Biological Structures 4:211–24. [LI]

L. Ingber (1982) Statistical mechanics of neocortical interactions: 1. Basic formulation. Physica D 5:83107. [LI]

L. Ingber (1983) Statistical mechanics of neocortical interactions: Dynamics of synaptic modification. Physical Review A 28:395416. [LI, PLN]

L. Ingber (1984b) Statistical mechanics of neocortical interactions: Derivation of shortterm-memory capacity. Physical Review A 29:3346–58. [LI]

L. Ingber (1984c) Statistical mechanics of nonlinear nonequilibrium financial markets. Mathematical Modelling 5:343–61. [LI]

L. Ingber (1985) Statistical mechanics of neocortical interactions: Stability and duration of the 7 ± 2 rule of short-term-memory capacity. Physical Review A 31:1183–86. [LI]

L. Ingber (1989) Very fast simulated re-annealing. Mathematical and Computer Modelling 12:967–73. [LI]

L. Ingber (1990) Statistical mechanical aids to calculating term structure models. Physical Review A 42:7057–64. [LI]

L. Ingber (1991) Statistical mechanics of neoeortical interactions: A scaling paradigm applied to electroencephalography. Physical Review A 44:4017–60. [LI]

L. Ingber (1992) Generic mesoscopic neural networks based on statistical mechanics of neocortical interactions. Physical Review A 45:2183–R2186. [LI]

L. Ingber (1994) Statistical mechanics of neocortical interactions: Path-integral evolution of short-term memory. Physical Review E 49:4652–64. [LI]

L. Ingber & P. L. Nunez (1990) Multiple scales of statistical physics of neocortex: Application to electroencephalogaphy. Mathematical and Computer Modelling 13:8395. [aJJW, LI]

L. Ingber & P. L. Nunez (1995) Statistical mechanics of neocortical interactions: High resolution pathintegral calculation of short-term memory. Physical Review E 51:5074–83. [LI, PLN]

M. Joliot , U. Ribary & R. Llinás (1994) Human oscillatory brain activity near 40 Hz coexists with cognitive temporal binding. Proceedings of the National Academy of Sciences USA 91:11748–51. [EK]

K. Kaneko (1990a) Globally coupled chaos violates the law of large numbers. Physical Review Letters 65:1391–94. [aJJW, ZJK, IT]

K. Kaneko (1990b) Clustering, coding, switching, hierarchical ordering, and control in a network of chaotic elements. Physica D 41:137–72. [IT]

K. Kaneko (1992) Mean field fluctuation in network of chaotic elements. Physica D 55:368–84. [aJJW, IT]

D. Kaplan & L. Glass (1992) Direct test for determinism in a time series. Physical Review Letters 68:427–30. [ZJK, WSP]

L. Kay , K. Shimoide & W. J. Freeman (1995) Comparison of EEG time series from rat olfactory system with model composed of nonlinear coupled oscillators. International Journal of Bifurcation and Chaos 5:849–58. [IT]

M. Kerszberg , S. Dehaene & J. P. Changeux (1992) Stabilization of complex input-output functions in neural clusters formed by synapse selection. Neural Networks 5:403–13. [AO]

K. Kishida (1982) Physical Langevin model and the time-series model in systems far from equilibrium. Physical Review A 25:496507. [LI]

K. Kishida (1984) Equivalent random force and time-series model in systems far from equilibrium. Jounal of Mathematical Physics 25:1308–13. [LI]

D. Kleinfeld (1986) Sequential state generation by model neural networks. Proceedings of National Academy of Sciences 83:9469–73. [rJJW]

F. Langouche , D. Roekaerts & E. Tirapegui (1982) Functional integration and semiclassical expansions. Reidel. [LI]

D. T. J. liley & J. J. Wright (1994) Intracortical connectivity of pyramidal and stellate cells: Estimates of synaptic densities and coupling symmetry. Network: Computation in Neural Systems 5:175–89. [arJJW]

J. E. Lisman & M. A. P. Idiart (1995) Storage of 7 ± 2 short-term memories in oscillatory subcycles. Science 267:1512–15. [LI]

W. A. Little & G. L. Shaw (1975) A statistical theory of short and long term memory. Behavioural Biology 14:115–33. [aJJW]

R. Llinás & U. Ribary (1993) Coherent 40-Hz oscillation characterized dream state in humans. Proceedings of the National Academy of Sciences USA 90:2078–81. [EK]

W. Lutzenberger , T. Elbert , W. J. Ray & N. Birbaumer (1993) The scalp distribution of the fractal dimension of the EEG and its variation with mental tasks. Brain Topography 5:2734. [MM]

K. Matsumoto & I. Tsuda 91983) Noise-induced order. Journal of Statistical Physics 31:87106. [IT]

W. S. McCulloch & W. H. Pitts (1943) A logical calculus of ideas immanent in nervous activity. Bulletin of Mathematical Biophysics 5:115–33. [HRE]

G. A. Miller (1956) The magical number seven, plus or minus two. Psychology Review 63:8197. [LI]

K. D. Miller , J. D. Keller & M. P. Stryker (1989) Ocular dominance column development: Analysis and simulation. Science 245:605–15. [AO]

R. Miller (1975) Distribution and properties of commissural and other neurons in cat sensorimotor cortex. Journal of Comparative Neurology 164:361–74. [RM]

M. Minsky (1993) Book review: Allen Newell, Unified theory of cognition. Artificial Intelligence 59:343–54. [EK, rJJW]

Y. Miyashita (1988) Neuronal correlate of visual associative long-term memory in the primate temporal cortex. Nature 335:817–20. [aJJW]

Y. Miyashita & H. S. Chang (1988) Neural correlate of pictorial short-term memory in the primate temporal cortex. Nature 331:6870. [aJJW]

M. Molnár (1994) On the origin of the P3 event-related potential component. International Journal of Psychophysiology 17:129–44. [MM]

M. Molnár , J. E. Skinner , V. Csépe , I. Winkler & G. Karmos (1995) Correlation dimension changes accompanying the occurrence of the msimatch-negativity and the P3 event-related potential component. Electroencephalography and Clinical Neurophysiology 95:118–26. [MM]

J. P. Nadal , G. Toulouse , J. P. Changeux & S. Dehaene (1986) Europhysics Letters 1(10):535–42. [aJJW]

I. Nebenzahl (1987) Recall of associated memories. Journal of Mathematical Biology 25:511–19. [aJJW]

P. L. Nunez (1989a) Generation of human EEG by a combination of long and short range neocortical interactions. Brain Topography 1:199215. [aJJW]

P. L. Nunez , R. B. Silberstein , P. J. Cadusch , R. S. Wijesinghe , A. F. Westdorp & R. Srinivasan (1994) A theoretical and experimental study of high-resolution EEG based on surface Laplacians and cortical imaging. Electrocncephalography and Clinical Neurophysiology 90:4057. [PLN]

P. L. Nunez & R. Srinivasan (1993) Implications of recording strategy for estimates of neocortical dynamics with electroencephalography. Chaos 3:257–66. [aJJW]

P. Peretto & J. J. Niez (1986) Collective properties of neuronal networks. In: Disordered systems and biological organisation, ed. E. Bienenstock , F. Fogelman-Soulie & G. Weisbuch . Springer-Verlag. [aJJW]

G. Pfurtscheller & R. Cooper (1975) Frequency dependence of the transmission of the EEG from cortex to scalp. Electroencephalography and Clinical Neurophysiology 38:9396. [PLN]

J. P. Pijn , J. van Neerven , A. Noest & F. H. Lopes da Silva 91991) Chaos or noise in EEG signals; dependence on state and brain site. Electroencephalography and Clincal Neurophysiology 79:371–81. [WSP]

W. S. Pritchard , D. W. Duke & K. K. Krieble (1995) Dimensional analysis of resting human EEG: 2. Surrogate-data testing indicates nonlinearity but now low-dimensional chaos. Psychophysiology 32:486–91. [ZJK, WSP]

P. E. Rapp , A. M. Albano , T. I. Schinah & L. A. Farwell (1993) Filtered noise can mimic low dimensional chaotic attractors. Physical Review E 47:2289–97. [LI]

P. E. Rapp , T. R. Bashore , J. M. Martineire , A. M. Albano , I. D. Zimmerrman & A. I. Mees (1989) Dynamics of brain electrical activity. Brain Topography 2:99118. [MM]

D. Ruelle (1994) Physics Today 47:2430. [aJJW]

G. Ruppeiner (1995) Riemannian geometry in thermodynamic fluctuation theory. Review of Modern Physics 67:605–59. [LI]

K. Sakai & Y. Miyashita (1991) Neural organisation for the long-term memory of paired associates. Nature 354:152–55. [aJJW]

J. S. Schiff , K. Jerger , D. H. Duong , T. Chang , M. L. Spano & W. L. Ditto (1994) Controlling chaos in the brain. Nature 370:615–20. [aJJW]

A. Schuz (1994) Patchiness as a means to get a message across. Trends in Neuroscience 17:365. [RMJ]

J. E. Skinner , M. Molnár & C. Tomberg (1994) The point correlation dimension: Performance with nonstationaiy surrogate data and noise. lntegrative Physiological and Behavior Science 29:217–34. [MM]

J. E. Skinner , M. Molnár , T. Vybiral & M. Mitra (1992) Application of chaos theory to biology and medicine. lntegrative Physiological and Behavioral Science 27:3953. [MM]

M. Steriade , P. Gloor , R. R. Llinas , F. H. Lopes da Silva & M. M. Mesulam (1990) Basic mechanisms of cerebral rhythmic activities. Electroencephalography and Clinical Neurophysiology 76:481508. [arJJW]

M. P. Stryker (1989) Is grandmother an oscillation? Nature 338:297–98. [aJJW]

R. W. Thatcher , P. J. Krause & M. Hrybyk (1986) Cortico-cortical associations and EEG coherence: A two-compartmental model. Electroencephalography and Clinical Neurophysiology 64:123–43. [aJJW, RM]

J. Theiler , S. Eubank , A. Longtin , B. Galdrikian & J. D. Farmer (1992) Testing for nonlinearity in time series: The method of surrogate data. Physica D 58:7794. [WSP]

M. J. Tovee & E. T. Rolls (1992) Oscillatory activity is not evident in the primate temporal visual cortex. Neuroreport 3:369–72. [aJJW]

I. Tsuda (1992) Dynamic link of memory-chaotic memory maps in non-equilibrium neural networks. Neural Networks 5:313–26. [aJJW]

I. Tsuda (1994) Can stochastic renewal of maps be a model for cerebral cortex? Physica D 75:165178. [aJJW]

I. Tsuda , E. Koemer & H. Shimuzu (1987) Memory dynamics in asynchronous neural networks. Progress in Theoretical Physics 78:5171. [aJJW, IT]

I. Tsuda & K. Matsumoto (1984) Noise-induced order: Complexity theoretical digression. In: Chaos and statistical methods, ed. Y. Kuramoto . Springer-Verlag. [IT]

A. van Rotterdam , F. H. Lopes da Silva , J. van Den Ende , M. A. Veirgever & A. J. Hermans (1982) A model of the spatiotemporal characteristics of the alpha rhythm. Bulletin of Mathematical Biology 44:283305. [rJJW, PLN, MJZ]

F. Ventriglia (1988) Computational simulation of cortical-like neural systems. Bulletin of Mathematical Biology 52:397429. [PÉ]

O. S. Vinogradova , E. S. Brazhnik , V. S. Stafekhina & V. F. Kitchigina (1993) Acetylcholine, theta-rhythm and activity of hippocampus: 2. Septal input. Neuroscience 53:971–79. [EK]

M. A. Whittington , R. D. Traub & J. G. R. Jeffreys (1995) Synchronized oscillations in interneuronal networks driven by metabotropic glutamate receptor activation. Nature 373:612–15. [HRE]

F. Wilczek (1994) A call for a new physics. Science 266:1737–38. [LI]

M. A. Wilson & J. D. Cowan (1973) A mathematical theory of the functional dynamics of cortical and thalamic nervous tissue. Kybernetik 13:5580. [aJJW, PLN]

J. J. Wright (1990) Reticular activation and the dynamics of neuronal networks. Biological Cybernetics 62:289–98. [aJJW]

J. J. Wright , R. R Kydd & A. A. Sergejew (1990a) Autoregression models of EEG. Biological Cybernetics 62:201–10. [arJJW]

J. J. Wright & D. T. J. Liley (1994) A millimetric-scale simulation of electrocortical wave dynamics based on anatomical estimates of cortical synaptic density. Network: Computation in Neural Systems 5:191202. [aJJW]

J. J. Wright & D. T. J. Liley (1995) Simulation of electrocortical waves. Biological Cybernetics 72:347–56. [arJJW]

J. J. Wright & A. A. Sergejew (1991) Radial coherence, wave velocity and damping of electrocortical waves. Electroencejrfialography and Clinical Neurophysiology 79:403–12. [arJJW]

J. J. Wright , A. A. Sergejew & D. T. J. Liley (1994) Computer simulation of electrocortical activity at millimetric scale. Electroencephalography and clinical Neurophysiology 90:365–75. [aJJW]

J. J. Wright , A. A. Sergejew & H. G. Stampfer (1990b) Inverse filter computation of the neural impulse giving rise to the auditory evoked potential. Brain Topography 2:293302. [aJJW]

X. Wu & H. Liljenström (1994) Regulating the nonlinear dynamics of olfactory cortex. Network: Computation in Neural Systems 5:4760. [HL]

Y. Yao & W. J. Freeman (1990) Model of biological pattern recognition with spatially chaotic dynamics. Neural Networks 3(2):153–70. [HRE]

M. N. Zhadin (1984) Rhythmic processes in cerebral cortex. Journal of Theoretical Biology 108:565–95. [PLN, MNZ]

G. Zhang & H. A. Simon (1985) STM capacity for Chinese words and idioms: Chunking and acoustical loop hypotheses. Memory & Cognition 13:193201. [LI]

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Behavioral and Brain Sciences
  • ISSN: 0140-525X
  • EISSN: 1469-1825
  • URL: /core/journals/behavioral-and-brain-sciences
Please enter your name
Please enter a valid email address
Who would you like to send this to? *



Full text views

Total number of HTML views: 0
Total number of PDF views: 19 *
Loading metrics...

Abstract views

Total abstract views: 238 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 18th October 2017. This data will be updated every 24 hours.