Biological Cybernetics

, Volume 92, Issue 6, pp 350–359 | Cite as

A field-theoretic approach to understanding scale-free neocortical dynamics

  • Walter J FreemanEmail author


A mesoscopic field-theoretic approach is compared with neural network and brain imaging approaches to understanding brain dynamics. Analysis of high spatiotemporal resolution rabbit electroencephalogram (EEG) reveals neural fields in the form of spatial patterns in amplitude (AM) and phase (PM) modulation of gamma and beta carrier waves that serve to classify EEGs from trials with differing conditioned stimuli (CS+/−). Paleocortex exemplified by olfactory EEG has one AM–PM pattern at a time that forms by an input-dependent phase transition. Neocortex shows multiple overlapping AM–PM patterns before and during presentation of CSs. Modeling suggests that neocortex is stabilized in a scale-free state of self-organized criticality, enabling cooperative domains to form virtually instantaneously by phase transitions ranging in size from a few hypercolumns to an entire hemisphere. Self-organized local domains precede formation of global domains that supervene and contribute global modulations to local domains. This mechanism is proposed to explain Gestalt formation in perception.


Phase Transition Conditioned Stimulus Brain Imaging Imaging Approach Local Domain 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Bak, P 1996How nature works: self-organized criticalityCopernicusNew YorkGoogle Scholar
  2. Barrett, TW 1993Electromagnetic phenomena not explained by Maxwell’s equationsLakhtakia, A eds. Essays on the formal aspects of electromagnetic theoryWorld Scientific PublishingSingaporeGoogle Scholar
  3. Barrett, TW 2000Topology and the physical properties of the electromagnetic fieldApeiron7311Google Scholar
  4. Barrett, TW 2001Topological approaches to electromagnetismEvans, M eds. Modern nonlinear optics, 2nd ednWiley InterscienceNew York699734Google Scholar
  5. Barrie, JM, Freeman, WJ, Lenhart, M 1996Modulation by discriminative training of spatial patterns of gamma EEG amplitude and phase in neocortex of rabbitsJ Neurophysiol76520539Google Scholar
  6. Braitenberg, V, Schüz, A 1991Anatomy of the cortex: statistics and geometrySpringerBerlin Heidelberg New YorkGoogle Scholar
  7. Freeman, WJ 1975Mass action in the nervous systemAcademicNew YorkAvailable in electronic form on http://sulcus.berkeley.eduGoogle Scholar
  8. Freeman, WJ 1987Simulation of chaotic EEG patterns with a dynamic model of the olfactory systemBiol Cybern56139150Google Scholar
  9. Freeman, WJ 2000Neurodynamics: an exploration of mesoscopic brain dynamicsSpringer-VerlagLondonGoogle Scholar
  10. Freeman, WJ 2003aA neurobiological theory of meaning in perception. Part 1. Information and meaning in nonconvergent and nonlocal brain dynamicsInt J Bifurc Chaos1324932511CrossRefMathSciNetGoogle Scholar
  11. Freeman, WJ 2003bA neurobiological theory of meaning in perception. Part 2. Spatial patterns of phase in gamma EEG from primary sensory cortices reveal the properties of mesoscopic wave packetsInt J Bifurc Chaos1325132535CrossRefMathSciNetGoogle Scholar
  12. Freeman, WJ 2003cThe wave packet: an action potential for the 21st centuryJ Integrat Neurosci2330CrossRefGoogle Scholar
  13. Freeman, WJ 2004aOrigin, structure, and role of background EEG activity. Part 1. Analytic phaseClin Neurophysiol11520772088CrossRefGoogle Scholar
  14. Freeman, WJ 2004bOrigin, structure, and role of background EEG activity. Part 2. Analytic amplitudeClin Neurophysiol11520892107CrossRefGoogle Scholar
  15. Freeman WJ (2005) Origin, structure, and role of background EEG activity. Part 3. Neural frame classification. Clin Neurophysiol (in press).Google Scholar
  16. Freeman WJ, Baird B (1987) Relation of olfactory EEG to behavior: spatial analysis: Behav Neurosci 101:393–408.Google Scholar
  17. Freeman, WJ, Barrie, JM 2000Analysis of spatial patterns of phase in neocortical gamma EEGs in rabbitJ Neurophysiol8412661278Google Scholar
  18. Freeman, WJ, Burke, BC 2003A neurobiological theory of meaning in perception. Part 4. Multicortical patterns of amplitude modulation in gamma EEGInt J Bifurc Chaos1328572866CrossRefGoogle Scholar
  19. Freeman, WJ, Burke, C, Holmes, MD 2003Aperiodic phase re-setting in scalp EEG of beta–gamma oscillations by state transitions at alpha-theta ratesHum Brain Mapp19248272CrossRefPubMedGoogle Scholar
  20. Freeman, WJ, Burke, BC, Holmes, MD, Vanhatalo, S 2003Spatial spectra of scalp EEG and EMG from awake humansClin Neurophysiol11410551060CrossRefGoogle Scholar
  21. Freeman, WJ, Chang, H-J, Burke, BC, Rose, PA, Badler, J 1997Taming chaos: stabilization of aperiodic attractors by noiseIEEE Trans Circuits Syst44989996CrossRefMathSciNetGoogle Scholar
  22. Freeman, WJ, Gaál, G, Jornten, R 2003A neurobiological theory of meaning in perception. Part 3. Multiple cortical areas synchronize without loss of local autonomyInt J Bifurc Chaos1328452856CrossRefGoogle Scholar
  23. Freeman, WJ, Grajski, KA 1987Relation of olfactory EEG to behavior: factor analysisBehav Neurosci101766777CrossRefPubMedGoogle Scholar
  24. Freeman, WJ, Rogers, LJ 2002Fine temporal resolution of analytic phase reveals episodic synchronization by state transitions in gamma EEGJ Neurophysiol87937945Google Scholar
  25. Freeman, WJ, Rogers, LJ 2003A neurobiological theory of meaning in perception. Part 5. Multicortical patterns of phase modulation in gamma EEGInt J Bifurc Chaos1328672887CrossRefGoogle Scholar
  26. Freeman, WJ, Rogers, LJ, Holmes, MD, Silbergeld, DL 2000Spatial spectral analysis of human electrocorticograms including the alpha and gamma bandsJ Neurosci Meth95111121CrossRefGoogle Scholar
  27. Freeman, WJ, Schneider, W 1982Changes in spatial patterns of rabbit olfactory EEG with conditioning to odorsPsychophysiol194456Google Scholar
  28. Freeman, WJ, Viana, Di Prisco G 1986Relation of olfactory EEG to behavior: time series analysisBehav Neurosci100753763CrossRefPubMedGoogle Scholar
  29. Friston, KJ 2000The labile brain. I, Neuronal transients and nonlinear coupling.Phil Trans R Soc Lond B355215236CrossRefGoogle Scholar
  30. Gibson, JJ 1979The ecological approach to visual perceptionHoughton MifflinBostonGoogle Scholar
  31. Haken, H 1983Synergetics: an introductionSpringerBerlin Heidelberg New YorkGoogle Scholar
  32. Herrick, CJ 1948The brain of the tiger salamanderUniversity of Chicago PressChicagoGoogle Scholar
  33. Houk J (2005) Agents of the mind. Biol Cybern (this issue)Google Scholar
  34. Jensen, HJ 1998Self-organized criticality: emergent complex behavior in physical and biological systemsCambridge UPNew YorkGoogle Scholar
  35. Köhler, W 1940Dynamics in psychologyGrove PressNew YorkGoogle Scholar
  36. Kozma, R, Freeman, WJ 2001Chaotic resonance: methods and applications for robust classification of noisy and variable patternsInt J Bifurc Chaos1023072322Google Scholar
  37. Kozma, R, Freeman, WJ 2002Classification of EEG patterns using nonlinear dynamics and identifying chaotic phase transitionsNeurocomputing4411071112CrossRefGoogle Scholar
  38. Kozma, R, Freeman, WJ 2003Basic principles of the KIV model and its application to the navigation problemJ Integr Neurosci2125145CrossRefPubMedGoogle Scholar
  39. Kozma, R, Freeman, WJ, Erdí, P 2003The KIV model – nonlinear spatio-temporal dynamics of the primordial vertebrate forebrainNeurocomput52819826Google Scholar
  40. Kozma R, Puljic M, Balister P, Bollabás B, Freeman WJ (2005) Phase transitions in the neuropercolation model of neural populations with mixed local and non-local interactions. Biol Cybern (this issue).Google Scholar
  41. Le, Quyen M, Foucher, J, Lachaux, J-P, Rodriguez, E, Lutz, A, Martinerie, J, Varela, F 2001Comparison of Hilbert transform and wavelet methods for the analysis of neuronal synchronyJ Neurosci Meth1118398CrossRefGoogle Scholar
  42. Linkenkaer–Hansen, K, Nikouline, VM, Palva, JM, Iimoniemi, RJ 2001Long-range temporal correlations and scaling behavior in human brain oscillationsJ Neurosci1513701377Google Scholar
  43. Mandelbrot, BB 1983The fractal geometry of natureFreemanSan FranciscoGoogle Scholar
  44. Miller, LM, Schreiner, CE 2000Stimulus-based state control in the thalamocortical systemJ Neurosci2070117016PubMedGoogle Scholar
  45. Ohl, FW, Scheich, H, Freeman, WJ 2001Change in pattern of ongoing cortical activity with auditory category learningNature412733736CrossRefPubMedGoogle Scholar
  46. Ohl FW, Deliano M, Scheich H, Freeman WJ (2003) Early and late patterns of stimulus-related activity in auditory cortex of trained animals. Biol Cybern, p 6. online: DOI 10.1007/s00422-002-0389-zGoogle Scholar
  47. Pessa, E 2000Cognitive modeling and dynamical systems theoryLa Nuova Critica15394Google Scholar
  48. Potapov, AB, Ali, MK 2001Nonlinear dynamics and chaos in information processing neural networksDiff Eq Dyn Syst9259319Google Scholar
  49. Prigogine, I 1980From being to becoming: time and complexity in the physical sciencesFreemanSan FranciscoGoogle Scholar
  50. Principe, JC, Tavares, VG, Harris, JG, Freeman, WJ 2001Design and implementation of a biologically realistic olfactory cortex in analog VLSIProc IEEE8910301051CrossRefGoogle Scholar
  51. Pikovsky, A, Rosenblum, M, Kurths, J 2001Synchronization – a universal concept in non-linear sciencesCambridge UPUKGoogle Scholar
  52. Quiroga RQ, KraskovA, KreuzT, Grassberger P (2002) Performance of different synchronization measures in real data: A case study on electroencephalographic signals. Physical Rev E, 6504:U645-U6 58-art. no. 041903Google Scholar
  53. Rodriguez, E, George, N, Lachaux, J-P, Martinerie, J, Renault, B, Varela, F 1999Perception’s shadow: long-distance synchronization of human brain activityNature397430433CrossRefPubMedGoogle Scholar
  54. Sholl, DA 1956The organization of the cerebral cortexWileyNew YorkGoogle Scholar
  55. Singer, W, Gray, CM 1995Visual feature integration and the temporal correlation hypothesisAnn Rev Neurosci18555586CrossRefPubMedGoogle Scholar
  56. Stam, CJ, Breakspear, M, Cappellen, van Walsum A-M, Dijk, BW 2003Nonlinear synchronization in EEG and whole-head recordings of healthy subjectsHum Brain Mapp196378CrossRefPubMedGoogle Scholar
  57. Tallon-Baudry, C, Bertrand, O 1999Oscillatory gamma activity in humans and its role in object representationTrends Cogn Sci3151162CrossRefPubMedGoogle Scholar
  58. Tass, P, Rosenblum, MG, Weule, J, Kurths, J, Pikovsky, AS, Volkmann, J, Schnitzler, A, Freund, H-J 1998Detection of n:m phase locking from noisy data: Application to magnetoencephalographyPhysical Rev Lett8132913294CrossRefGoogle Scholar
  59. Tolman, EC 1948Cognitive maps in rats and menPsychol Rev55189208Google Scholar
  60. Tsuda, I 2001Toward an interpretation of dynamics neural activity in terms of chaotic dynamical systemsBehav Brain Sci24793847PubMedGoogle Scholar
  61. Varela, F, Lachaux, J-P, Rodriguez, E, Martinerie, J 2001The brain-web: phase synchronization and large-scale integrationNat Rev Neuro2229239CrossRefPubMedGoogle Scholar
  62. Vitiello, G 2001My double unveiled. The dissipative quantum model of brainBenjaminAmsterdamGoogle Scholar
  63. Wang, XF, Chen, GR 2003Complex networks: small-world, scale-free and beyondIEEE Circuits Syst31620Google Scholar
  64. Watts, DJ, Strogatz, SH 1998Collective dynamics of ‘small-world’ networksNature393440442CrossRefPubMedGoogle Scholar

Copyright information

© Springer-Verlag 2005

Authors and Affiliations

  1. 1.Department of Molecular & Cell BiologyUniversity of California at BerkeleyBerkeleyUSA

Personalised recommendations