Metastability, Criticality and Phase Transitions in brain and its Models

Werner, MD Gerhard (2006) Metastability, Criticality and Phase Transitions in brain and its Models. [Preprint]

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This essay extends the previously deposited paper "Oscillations, Metastability and Phase Transitions" to incorporate the theory of Self-organizing Criticality. The twin concepts of Scaling and Universality of the theory of nonequilibrium phase transitions is applied to the role of reentrant activity in neural circuits of cerebral cortex and subcortical neural structures.

Item Type:Preprint
Keywords:self-organizing criticality, phase transitions, scaling, universality, reentrant neural circuits
Subjects:Computer Science > Dynamical Systems
Computer Science > Complexity Theory
Computer Science > Artificial Intelligence
Biology > Theoretical Biology
ID Code:5129
Deposited By: Werner, Gerhard
Deposited On:08 Sep 2006
Last Modified:11 Mar 2011 08:56

References in Article

Select the SEEK icon to attempt to find the referenced article. If it does not appear to be in cogprints you will be forwarded to the paracite service. Poorly formated references will probably not work.

Acebron, J.A., Bonilla, L.L, Perez, C.J., Ritort, F., Spigler, R., 2005. The Kuramoto model: a simple paradigm

for synchronization phenomena. Rev Mod Phys 77,137-185.

Albert, R., Barabasi, A.L., 2002. Statistical mechanics of complex networks. Rev Mod Phys 74,47-97.

Ashby, R., 1960. Design for a brain. Chapman & Hall, London.

Baars, B.J., 1988. A cognitive theory of consciousness. Cambridge University Press, Cambridge.

Baars, B.J., 1997. In the theater of consciousness. Oxford University Press, New York.

Baars, B.J., 2002. The conscious access theory: origins and recent evidence. Trends Cogn Sci. 6,47-52.

Bakhman, T., 2000. Microgenetic approach to the conscious Mind. John Benjamins Publishing Company,


Bak, P., 1996. How Nature works: the science of self-organized criticality. Copernicus, New York.

Bartels, A., Zeki, S., 2004. The chronoarchitecture of human brain – natural viewing conditions reveal a time-

based anatomy of the brain. NeuroImage 22,419-433.

Basar, E. 1983, Toward a physical approach to integrative Physiology: brain dynamics and physical causality. Amer.J.Physiol.245, R510-R533.

Bauer, H.U., Pawelzik, K., 1993. Alternating oscillatory and stochastic dynamics in a model for a

Neuronal assembly. Physica D 69,380-393.

Beggs, J. M., Plenz, D. ,2003. Neuronal avalanches in neocortical circuits. J. Neurosci 23,11167-11177.

Beggs, J. M., Plenz. D., 2004. Neuronal avalanches are diverse and precise activity patterns that are stable for

many hours in cortical slice cultures. J. Neurosci. 24,5216-5229.

Bienenstock, E., Lehmann, D., 1998. Regulated criticality in the brain ? Adv. Complex Systems 1:361-384.

Binney, J., 1992. The theory of critical phenomena. Clarendon Press, Oxford.

Blanchard, P., Cessac, B., Kruger, T., 2000. What can one learn about self-organized criticality from

Dynamical system theory ? J. Statist. Phyics 98,375-404.

Bornholdt, S., Rohl, T., 2003. Self-organized critical networks, Physical Review E 67,066118.

Bornholdt, S., Rohlf, T., 2000.Topological evolution of dynamical networks: global criticality from local

dynamics, Phys. Rev. Lett. 84,6114-6117.

Braeutigam, S., Rose, S.P.R., Swithenby, S.J., Ambler, T., 2004. The distributed neural systems supporting

choice - making in real-life situations: differences between men and women when choosing groceries

detected using magnetoencephalography. Europ. J Neurosci, 1-10.

Bressler, S.L., 1995. Large-Scale cortical networks and cognition. Brain Res. Rev. 20,288-304.

Bressler, S.L., Kelso, J.A.S., 2001. Cortical coordination dynamics and cognition. Trends Cogn Sci. 5,26-


Changeux, J-P., 1983. L’homme neuronal. Fayard, Paris.

Changeux, J-P., Dehaene, S., 1989. Neuronal models of cognitive functions. Cognition 33,63-109.

Chialvo, D.R., 2004. Critical brain networks. Physica A 340,756-765.

Cosmelli, D., Lachaux, J-P. Thompson, E., 2006. Neurodynamics of consciounsess, forthcoming in:

The Cambridge Handbook of Consciousness, Zelazo, P.D. , Moscovitch, M., Thomson, E.,edits.

Da Silva, L., Papa, A.R.R., de Souza, A.M.C., 1998. : Criticality in a simple model for brain functioning

Physics Letters A 242,342-348.

Dehaene, S., Naccache, L., 2001. Towards a cognitive neuroscience of consciousness: basic evidence and a

workspace framework. Cognition 79, 1-37.

Dehaen, S., Changeux, J-P., Nadal, J-P., 1987. Neural networks that learn temporal sequences by selection. Proc

Natl Acad Sci USA 84,2727-2731.

Deahaene. S,, Changeux, J-P., 1997. A hierarchical neuronal network for planning behavior. Proc Natl Acad Sci

USA 94,13293-13298.

Dehaene, S., Kerszberg, M., Changeux, J-P., 1998. A neuronal model of a global workspace in effortful cognitive

tasks. Proc Natl Acad Sci USA 95,14529-14534.

Dehaene, S, Sergent, C., Changeux, J-P., 2003. A neuronal network model linking subjective reports and

objective physiological data during conscious perception. Proc Natl Acad Sci USA 100,8520-8525.

Deahaene, S., Changeux, J-P., 2004. Neuronal mechanisms for access to consciousness. In M Gazzaniga ed. The

Cognitive Neurosciences , 3rd edit, Norton, N.Y., pp.1145-1157.

Dehaene, S., Changeux, J-P., 2005. Ongoing spontaneous activity controls access to consciousness: a neuronal

model for inattentional blindness. PLoS 3(5), e141.

Dickman, Rp, Munoz, M. A., Vespignani, A., Zapperi, S.,2002/2006. Paths to self-organized criticality,

arXiv:cond-mat/9910454 v2

Ding, M., Bressler ,S.L., Yang, W., Liang, H., 2000. Short-window spectral analysis of cortical event-related

potentials by adaptive multivariate autoregressive modeling: data processing, model validation, and

variability assessment. Biol Cybern 83,35-45.

Eckhorn, R., Bauer, R., Jordan, W., Broisch, M., Kruse, W., Munk, M., Reitboeck, H.J., 1988. Coherent

oscillations: a mechanism for feature linking in the visual cortex. Biol Cybern 60,121-130.

Edelman, G.M., 1987. Neural Darwinism: the theory of neural group selection. Basic Books, NY.

Edelman, G.M., 1989. The remembered present: a biological theory of consciousness. Basic Books, NY.

Edelman, G.M., 1993. Neural Darwinism: selection and reentrant signaling in higher brain function. Neuron 10,115-125.

Edelman, G.M., Tononi, G., 2001. Consciousness: how matter becomes Imagination. Penguin, London.

Edelman, G. M.: 2003. Naturalizing consciousness: a theoretical framework. Proc Natl Acad Sci USA


Eguiluz, V.M., Chialvo, D.R., Cecchi, G,, Baliki, M., Apkarian, A.V., 2005. Scale-free Brain functional networks.

Phys. Rev. Lett. 94,018102-1.

Engel, A.K., Fries, P., Koenig, P., Brecht, M,, Singer, W,, 1999. Temporal binding, Binocular Rivalry, and

Consciousness. Consciousness and Cognition 8,128-151.

Erdos, P., Renyi, A., 1960. Publications of the Mathematical Institute of the Hungarian Academy of Sciences


Fingelkurts, A .A., Fingelkurts, A. A., 2001. Operational architectonics of the human brain biopotential field:

Towards solving the mind-brain Problem. Mind and Brain 2,262-296.

Fingelkurts, A. A. , Fingelkurts, A. A.,2004. Making complexity simpler: multivariability and metastability

in the brain. Internat J.Neurosci 114,843-862.

Fingelkurts ,An.A., Fingelkurts Al.A., Kivisaari,R., Pekkonen,E, Ilmoniemi, R.J., Kahkonen, S.A.,2004, Local and remote functional connectivity of neocortex under the inhibition influence. NeuroImage 22, 1390-1406.

Fingelkurts, A. A., Fingelkurts, A. A., 2005. Mapping of the brain operational architectonics. pp 59-98, in: F J

Chen, ed , Focus on brain mapping research, Nova Science Publ.

Fingelkurts, A.A., Fingelkurts, A.A., 2006. Timing in cognition and EEG brain dynamics: discreteness versus

continuity. Cogn.Process 7,135-162.

Flyvbjerg, H., 1996. Simplest possible self-organized critical system. Phys Rev Lett 76,940-943.

Fox, M.D., Snyder, A.Z., Vincent, J.L, Corbetta, M., van Essen, D.C., Raichle, M.E., 2005. The human

brain is intrinsically organized into dynamic, anticorrelated functional networks. Proc Natl Acad Sci

USA 102,9673-9678.

Franklin, S., Graesser, A., 1999. A software agent model of consciousness. Consciousness and Cognition


Franklin, S., 2003. IDA: a conscious artifact ? J. Consciousness Studies 10,47-66.

Freeman, W.J., 1975. Mass action in the nervous system. Academic Press NY.

Freeman, W.J., Barrie, J.M.,1994. Chaotic oscillations and the genesis of meaning in cerebral cortex,, in:

G. Buzsaki, R. Llinas W.Singer, Temporal Coding in the brain, pp 13-37.

Freeman, W.J., 2000. Neurodynamics. Springer, New York.

Freeman, W.J . 2003. The wave packet: an action potential for the 21st century J.Integr. Neurosci. 2,3-30.

Freeman, W.J., 2004. Origin, structure and role of background EEG activity, Clin Neurophysiol 116,1117-


Freeman, W.J., 2005. A field-theoretic approach to understanding scale-free neocortical dynamics

Biol.Cybern. 92350-359

Freeman, W.J., Holmes, M.D., 2005. Metastability, instability, and state transitions in neocortex. Neural

Networks 18,497-504.

Freeman, W.J., Vitiello, G., 2006. Nonlinear brain dynamics as macroscopic manifestation of underlying

many-body Field dynamics. Physics of Life Reviews 3,93-118

Frigg, R., 2003. Self-organized criticality –what it is and what it isn’t Stud. Hist. Phil. Sci 34,613-632.

Friston, K.J., 1997. Transients, metastability, and neuronal dynamics. NeuroImage 5,164-171.

Friston, K.J. (2000) The labile brain I. Proc R Soc Lond , Biology, 355,215-236.

Gisiger, T., 2001. Scale invariance in biology: coincidence or footprint of a universal mechanism ? Biol.

Rev. 76,161-209.

Gray, C.M., Singer, W., 1987. Neurosci.Abst. 404:3.

Gray, C.M., Koenig, P., Engel, A.K., Singer, W., 1989. Oscillatory responses in cat visual cortex exhibit

intercolumnar synchronization which reflects global stimulus properties. Nature 338,334-337.

Gray, M.G., Singer, W., 1989. Stimulus-specific neuronal oscillations in orientation columns of cat visual cortex.

Proc Nat Acad Sci USA 86,1698-1702.

Griffith, J. S. , 1963.On the stability of brain-like structures, Biophysical J. 3,299-308.

Grinstein, G., 1995. Generic scale invariance and self-organized criticality, pp. 261-293, in:

A, McKane, M. Droz J Vannimenus D. Wolf, Scale invariance, interfaces and non-equilibrium

Dynamics, Plenum Press NY.

Grimmett, G., 1989. Percolation, Springer N.Y.

Haken, H., 1983. Introduction. In E Basar, H Flohr, H,Haken eds., Synergetics of the brain. Springer Berlin.

Haken, H., 2002. Brain dynamics. Springer, NY.

Haldeman, C., Beggs, J. M. , 2005. Critical branching captures activity in living neural networks and maximizes

the Number of metastable states. Phys. Rev. Lett. 94, 058101-1/058101.

Izhikevitch, E.M. , Gally, J. A., Edelman, G.M., 2004. Spike timing dynamics of neuronal groups. Cerebral

Cortex 14,933-944.

Jensen, H. J., 1998. Self-organized criticality. Cambridge University Press.

Kadanoff, L.P., Goetze, W., Hamblen, D., Hecht, R., Lewis, E.A.S., Palciauskas, V.V. , Rayl, M., Swift, L.,

1967. Static phenomena near critical points: theory and experiment. Rev. Modern Physics 39,395-431.

Kadanoff, L. P., Nagel, S. R., Wu, L., Zhou, S., 1989. Scaling and universality in avalanches. Physical Rev A


Kadanoff, L.P., 1990. Scaling and universality in statistical physics. Physica A 163:1-14.

Kaplan, A.Y.A., Fingelkurts, A.A., Fingelkurts, A.A., Darkhovsky, B.S., 1997. Topological mapping of sharp

reorganization synchrony in multichannel EEG. Am J Electroneurodiagostic Technol. 37,265-275.

Katachalsy, A., Rowland, V., Huberman, B., 1974. Neuroscience Res.Program Bull 12.

Kelso, J.A.S., Bressler, S.L., Buchanan, S., DeGuzman, G.C., Ding, M., Fuchs, A., Holroyd, T., 1992. Phase

transition in brain and human behavior. Phys Lett A 169, 134-144.

Kelso, J.A.S.,1959. Dynamic patterns: the self-organization of brain and behavior. MIT Press, Cambridge MA.

Kelso, J.A.S., Engstrom, D.A., 1006. The complementary nature. MIT Press, Cambridge, MA.

Kentridge, R.W., 1993. Dissipative structures and elf-organizing criticality in neural networks with spatially

localized connectivity, p. 531-535, in: F.H. Eeckman & J.M. Bower, Kluver Academic Press Boston.

Kozma, R., Puljic, M., Balister, P., Bollobas, B., Freeman, W.J., 2005. Phase transitions in the neuropercolation

model of neural populations with mixed local and non-local interactions. Biol. Cyber. 92:367-379.

Kuramoto,Y., 1984. Chemical oscillations, waves and turbulence. Dover Publ., N.Y.

Lamme, V.A.F., Roelfsema, P.R., 2000. The distinct modes of vision offered by feed-forward and recurrent

processing. TINS 23,571-579.

Lehman, D, Strik WK, Henggeler B, Koenig T, Koukkou, M., 1998. Brain electric microstates and momentary

conscious mind states as building blocks of spontaneous thinking: I. Visual imagery and abstract thoughts.

Internat J Psychophysiol 29:1-11

Lehman, D., Faber, P.L., Gianotti, L.R.R., Kochi, K., Pascual-Marqui, R.D., 2006. Coherence and phase

Locking in the scalp EEG and between LORETA model sources, and microstates as putative

Mechanisms of brain temporo-spatial functional organization. J. Physiol.Paris 99,29-36.

Le vanQuyen, M., 2003. Disentangling the dynamic core: a research program for a neurodynamics at a large

scale. Biol Res 36,67-88.

Linkenkaer-Hansen, K., Nikouline, V.V., Palva, J.M, Ilmoniemi, R.J., 2001. Long –range temporal correlations

and Scaling behavior in human brain oscillations. J. Neurosci. 21, 1370-1377.

Libet, B., 2004. Mind time: the temporal factor in consciousness. Harvard University Press, Cambridge, Mass.

Llinas, R., Ribary, U., Contreras, D., Pedroarena, C., 1998. The neuronal basis of consciousness. Phil Trans R Soc

Lond B 353,1841-1849,

Lumer, E.D., Edelman, G.M., Tononi, G., 1997. Neural dynamics in a model of the thalamocortical system. I.

Layers, loops, and the emergence of fast synchronous rhythms. Cerebral Cortex 7,207-227.

Lutz, A., Lachaux, J-P., Martineri, J., Varela, F.J., 2002. Guiding the study of brain dynamcis by using first-

person data: synchrony patterns correlate with ongoing conscious states during simple visual tasks. Proc

Natl Acad Sci USA 99,1586-1591.

McComb, W.D., 2004. Renormalization Methods. Clarendon Press, Oxford

McKenna, T. M., McMullen, T. A., Shlesinger, M..F., 1994. The brain as a dynamical physical system,

Neuroscience 60,587-605.

Murthy, V.N., Fetz, E.E., 1992. Coherent 25-35 Hz oscillations in the sensorimotor cortex of awake behaving

monkeys. Proc Natl Acad Sci USA 89,5670-5674.

Newell, A., 1994. Unified theories of cognition: The William James Lectures, Harvard University Press,

Cambridge Mass.

Newman, J., Baars, B.J., 1993. A neural attentional model for access to consciousness: a global workspace

perspective. Concepts in Neuroscience 4, 255-290.

Newman, J., Baars, B.J., Cho, S-B., 1997. A neural global workspace model for conscious attention. Neural

Networks 10,1195-1197.

Newman, J., 2003. The structure and function of complex networks. SIAM Review 45,167-256.

Odor, G., 2004. Universality classes in nonequilibrium lattice systems , Revs Modern Physics 76,663-724.

Olam, Z., Feder, H. J. S., Christensen, K., 1992. Self-organized crtiticality in a continuous nonconservative

cellular automaton modeling earthquales Phys. Rev. Lett. 68, 1244-1247. .

Paczuski, M., Maslov, S., Bak, P., 1996. Avalanche dynamics in evolution, growth and depinning models,

Physical Rev. E 53,414-443.

Pietronero, L., Vespignani, A., Zapperi, S., 1994. : Renormalization scheme for self-organized criticality in

sandpile models Phys. Rev. Lett. 72,690-1693.

Rapoport, A.,1952. “Ignition” phenomena in random nets, Bull Mathemat. Biol. 14,35-44.

Ribary, U., Ionnaides, A.A., Singh, K.D., Hasson, R., Bolton, J.P.R., Lado, F., Mogilner. A., Llinas. R., 1991.

Magnetic field tomography of coherent thalamocortical 40-Hz oscillations in humans. Proc Natl Acad Sci

USA 88,11037-11041.

Roelfsema, P.R., Engel, A.K., Koening, P., Singer, W., 1997. Visuomotor integration is associated with zero-lag

synchronization among cortical areas. Nature 385,157-161.

Rodriguez, E., George, N., Lachaux, J-P., Martineri, J., Renault, B., Varela, F.J., 1999. Perception’s shadow:

long distance synchronization of human brain activity. Nature 397,430-433.

Schmolensky, M.T., Wang, Y., Hanes, D.P., Thompson. K.G., Leutgeb, S., Schall, J.D., Leventhal, A.G., 1998.

Signal timing across macaque visual system. J. Neurophysiol. 79,3272-3278.

Sergent, C., Dehaene, S., 2004. Is consciousness a gradual phenomenon ? Psychol Sci 15,720-728.

Seth, A.K., 2005. Causal connectivity of evolved neural networks during behavior. Network: Computation in Nervous Systems 16,35-54.

Seth, A.K., Baars, B.J., 2005. Neural Darwinism and consciousness, Consciousness and Cognition 14, 140-168.

Seth,A.K.,Izhikevich,E.,Reeke, G.N., Edelman, G.M.,2006. Theories and measures of consciousness: an extended framework. Proc>Nat.Acad.Sci.USA 103,10799-10804.

Sigman M., Dehaene, S., 2005. Parsing a cognitive task: a characterization of the Mind’s bottleneck. PLoS 3(2), e37.

Singer, W., Engel, A.K., Kreiter, A.K., Munk, M.H.J., Neuenschwander, S., Roelfsema, P.R., 1997. Neuronal

assemblies: necessity, signature and detectability. Trends Cogn Sci 1,252-261.

Singer, W., 1998. Consciousness and the structure of neuronal representations. Phil Trans R Soc Lond B , 353,1829-1840.

Sporns, O., Tononi, G., Edelman, G.M., 1991. Modeling perceptual grouping and figure-ground segregation by

means of active re-entrant connections. Proc Natl Acad Sci USA 88,129-133.

Sporns, O., Tononi, G., Edelman, G.M., 2000. Connectivity and complexity: the relationship between

neuroanantomy and brain dynamics. Neural Networks 13,909-922.

Sporns, O., Koetter, R., 2004. Motifs in brain networks. PLoS Biology, 2(11), e369.

Sporns, O., Chialvo, D.R., Kaiser, M., Hilgetag, C.C., 2004. Organization, development and function of complex

brain networks. Trends in Cog. Sci. 8,418-425.

Sporns, O.,(2004. Complex neural dynamics. In: VK Jirsa,& JAS Kelso, ed. Coordination Dynamics: issues and

trends. Springer, Berlin.

Stauffer, D., Aharony, A., 1991/94. Introduction to percolation theory. CRC Press Boca Raton.

Tallon-Baudry, C., Bertrand, O., 1999. Oscillatory gamma activity in humans and its role in object representation.

Trends Cogn Sci 3,151-162.

Taylor, J.G,, Alavi, F.N., 1993. Mathematical analysis of a competitive networks for attention. In: J.G. Taylor,

Mathematical Approaches to neural networks, Amsterdam: Elsevier Publ.

Tononi, G., Edelman, G.M., 1998. Consciousness and complexity. Science 282,1846-1851.

Tononi, G., Edelman, G.M., 2000. A Universe of consciousness: how matter becomes imagination. Basic Books, N.Y.

Tononi, G., Sporns, O., Edelman, G.M., 1992. Reentry and the problem of integrating multiple cortical areas:

Simulation of dynamic integration in the visual system. Cerebral Cortex 2,310-335.

Tononi, G., Sporns, O., Edelman, G.M., 1994. A measure for brain complexity: relating functional segregation

and integration in the nervous system. Proc Natl Acad Sci USA, 91,5033-5037.

Tononi, G., Edelman, G.M., Sporns, O., 1998. Complexity and coherency: integrating information in the brain.

Trends Cogn Sci 2,474-484.

Tononi, G., Sporns, O., 2003. Measuring information integration. BMC Neuroscience 4,31

available at: .

Tononi,G., 2004. An information integration theory of consciousness. BMC Neuroscience 5,42.

Turing, A. M., 1950. Computing machinery and intelligence Mind 59,433-460.

Usher, M., Stemmler, M., Olami, Z., 1995. Dynamic pattern formation leads ti 1/f noise in neural populations

Phys. Rev. Lett. 74,326-329.

Varela, F.J., Lachaux,J-P., Rodriguez, E., Martineri, J., 2001. The brainweb: phase synchronization and large-

scale integration. Nat Rev Neurosci 2,29-239.

Vespignani, A.S., Zapperi, S., Pietronero, L., 1995. Renormalization approach to self-organized critical behavior

of sandpile models. Physical Rev E 51,1711-1751.

Vogels, T.P., Rajan, K., Abbott, L.F., 2005. Neural network Dynamics. Annu. Rev. Neurosci. 28,357-376.

von Stein, A., Sarntheim, J., 2000. Different frequencies for different scales of cortical integration: from local

gamma to long range alpha/theta synchronization. Int. J. Psychophysiol. 38,301-313.

Wakeling, J., 2003. Order-disorder transition in the Chialvo-Bak ‘minibrain’ controlled by network geometry.

Physica A 325,561-569.

Wallace, R., 2005 a. Consciousness: a mathematical treatment of the Neuronal Global Workspace Model.

Springer, NY.

Wallace, R., 2005 b. A modular network treatment of Baars’ Global Workspace consciousness model (Version

7.2). available at:

Wallace, R., 2005 c. A Global Workspace perspective on mental disorders, Theoretical Biology and Medical

Modeling. available at:

Wallace, R., 2006. Generalized inattentional blindness from a Global Workspace perspective. available at:

Werner, G., 2004. The siren call of metaphor: subverting the proper task of Neuroscience. J. Integrative Neurosci.


Werner, G., 2005. Perspectives on the Neuroscience of Cognition and Consciousness. BioSystems, in print.

Wilson, K. G., 1979. Problems in physics with many scales, Scientific American 241,149-157 (August).

Zhao, X-W., Chen, T-L., 2003. Different avalanche behaviors in different specific areas

of a system based on neural networks. Commun Theoret Phys 40,363-368.


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