Is there chaos in the brain?

Abstract For some years there has been a controversy about whether brain state variables such as EEG or neuronal spike trains exhibit chaotic behaviour. Wright & Liley claim that the local dynamics measured by spike trains or local field potentials exhibit chaotic behaviour, but global measures like EEG should be governed by linear dynamics. We propose a different scheme. Based on simulation studies and various experiments, we suggest that the pointwise dimension of EEG time series may provide some valuable information about underlying neuronal generators.

[1]  Sholl Da.  Dendritic organization in the neurons of the visual and motor cortices of the cat. , 1953 .

[2]  A. M. Uttley.  The probability of neural connexions , 1955, Proceedings of the Royal Society of London. Series B - Biological Sciences.

[3]  G. A. Miller.  THE PSYCHOLOGICAL REVIEW THE MAGICAL NUMBER SEVEN, PLUS OR MINUS TWO: SOME LIMITS ON OUR CAPACITY FOR PROCESSING INFORMATION 1 , 1956 .

[4]  Bryce S. DeWitt,et al.  Dynamical theory in curved spaces. 1. A Review of the classical and quantum action principles , 1957 .

[5]  W. Freeman,et al.  A LINEAR DISTRIBUTED FEEDBACK MODEL FOR PREPYRIFORM CORTEX. , 1964, Experimental neurology.

[6]  R. Stacy,et al.  Computers in biomedical research , 1967 .

[7]  Walter J. Freeman,et al.  Prepyriform electrical activity after loss of peripheral or central input, or both ☆ , 1968 .

[8]  Shun-ichi Amari,et al.  Learning Patterns and Pattern Sequences by Self-Organizing Nets of Threshold Elements , 1972, IEEE Transactions on Computers.

[9]  W J Freeman,et al.  Measurement of oscillatory responses to electrical stimulation in olfactory bulb of cat. , 1972, Journal of neurophysiology.

[10]  G Pfurtscheller,et al.  Frequency dependence of the transmission of the EEG from cortex to scalp. , 1975, Electroencephalography and clinical neurophysiology.

[11]  Robert Miller,et al.  Distribution and properties of commissural and other neurons in cat sensorimotor cortex , 1975, The Journal of comparative neurology.

[12]  W A Little,et al.  A statistical theory of short and long term memory. , 1975, Behavioral biology.

[13]  Donald O. Walter,et al.  Mass action in the nervous system , 1975 .

[14]  F. H. Lopes da Silva,et al.  Models of neuronal populations: the basic mechanisms of rhythmicity. , 1976, Progress in brain research.

[15]  Grégoire Nicolis,et al.  Self-Organization in nonequilibrium systems , 1977 .

[16]  G. Pfurtscheller.  Handbook of electroencephalography and clinical neurophysiology , 1978 .

[17]  V. Braitenberg.  Cell Assemblies in the Cerebral Cortex , 1978 .

[18]  M. Brazier,et al.  Architectonics of the cerebral cortex , 1978 .

[19]  Roland Heim,et al.  Theoretical Approaches to Complex Systems , 1978 .

[20]  P. Seglar,et al.  Stochastic Processes in Nonequilibrium Systems , 1978 .

[21]  W. Freeman,et al.  Frequency analysis of olfactory system EEG in cat, rabbit, and rat. , 1980, Electroencephalography and clinical neurophysiology.

[22]  E. Donchin.  Presidential address, 1980. Surprise!...Surprise? , 1981, Psychophysiology.

[23]  Lester Ingber,et al.  Towards a unified brain theory , 1981 .

[24]  A. J. Hermans,et al.  A model of the spatial-temporal characteristics of the alpha rhythm , 1982 .

[25]  E. Tirapegui,et al.  Functional Integration and Semiclassical Expansions , 1982 .

[26]  J J Hopfield,et al.  Neural networks and physical systems with emergent collective computational abilities. , 1982, Proceedings of the National Academy of Sciences of the United States of America.

[27]  L. Ingber.  Statistical Mechanics of Neocortical Interactions. I. Basic Formulation , 2001 .

[28]  Kuniharu Kishida,et al.  Physical Langevin model and the time-series model in systems far from equilibrium , 1982 .

[29]  J. D. Farmer,et al.  Information Dimension and the Probabilistic Structure of Chaos , 1982 .

[30]  Lester Ingber,et al.  Statistical mechanics of neocortical interactions. Dynamics of synaptic modification , 1983 .

[31]  Ichiro Tsuda,et al.  Noise-induced order , 1983 .

[32]  S. Bressler,et al.  Shadows of thought: shifting lateralization of human brain electrical patterns during brief visuomotor task. , 1983, Science.

[33]  P Erdi,et al.  Hierarchial thermodynamic approach to the brain. , 1983, The International journal of neuroscience.

[34]  P. Grassberger,et al.  Measuring the Strangeness of Strange Attractors , 1983 .

[35]  M. Zhadin.  Rhythmic processes in the cerebral cortex. , 1984, Journal of theoretical biology.

[36]  J J Hopfield,et al.  Neurons with graded response have collective computational properties like those of two-state neurons. , 1984, Proceedings of the National Academy of Sciences of the United States of America.

[37]  Lester Ingber,et al.  Path-integral Riemannian contributions to nuclear Schrödinger equation , 1984 .

[38]  Kuniharu Kishida,et al.  Equivalent random force and time‐series model in systems far from equilibrium , 1984 .

[39]  L. Ingber.  Statistical mechanics of neocortical interactions. Derivation of short-term-memory capacity , 1984 .

[40]  Yoshiki Kuramoto,et al.  Chaos and Statistical Methods , 1984 .

[41]  Lester Ingber,et al.  Statistical mechanics of nonlinear nonequilibrium financial markets , 1984 .

[42]  Ingber,et al.  Statistical mechanics of neocortical interactions: Stability and duration of the 7+/-2 rule of short-term-memory capacity. , 1985, Physical review. A, General physics.

[43]  W. Freeman,et al.  Spatial EEG patterns, non-linear dynamics and perception: the neo-sherringtonian view , 1985, Brain Research Reviews.

[44]  H. Simon,et al.  STM capacity for Chinese words and idioms: Chunking and acoustical loop hypotheses , 1985, Memory & cognition.

[45]  Stanislas Dehaene,et al.  Networks of Formal Neurons and Memory Palimpsests , 1986 .

[46]  J. Hopfield,et al.  Computing with neural circuits: a model. , 1986, Science.

[47]  G. Parisi.  A memory which forgets , 1986 .

[48]  D Kleinfeld,et al.  Sequential state generation by model neural networks. , 1986, Proceedings of the National Academy of Sciences of the United States of America.

[49]  G. Parisi,et al.  Asymmetric neural networks and the process of learning , 1986 .

[50]  Françoise Fogelman-Soulié,et al.  Disordered Systems and Biological Organization , 1986, NATO ASI Series.

[51]  R. Thatcher,et al.  Cortico-cortical associations and EEG coherence: a two-compartmental model. , 1986, Electroencephalography and clinical neurophysiology.

[52]  Ichiro Tsuda,et al.  Memory Dynamics in Asynchronous Neural Networks , 1987 .

[53]  I. Nebenzahl.  Recall of associated memories , 1987, Journal of mathematical biology.

[54]  S Dehaene,et al.  Neural networks that learn temporal sequences by selection. , 1987, Proceedings of the National Academy of Sciences of the United States of America.

[55]  W. Freeman,et al.  How brains make chaos in order to make sense of the world , 1987, Behavioral and Brain Sciences.

[56]  Walter J. Freeman,et al.  Strange attractors that govern mammalian brain dynamics shown by trajectories of electroencephalographic (EEG) potential , 1988 .

[57]  Y. Miyashita,et al.  Neuronal correlate of pictorial short-term memory in the primate temporal cortexYasushi Miyashita , 1988, Nature.

[58]  Y. Miyashita.  Neuronal correlate of visual associative long-term memory in the primate temporal cortex , 1988, Nature.

[59]  F. Ventriglia.  Computational simulation of activity of cortical-like neural systems , 1988 .

[60]  R. Verleger.  Event-related potentials and cognition: A critique of the context updating hypothesis and an alternative interpretation of P3 , 1988, Behavioral and Brain Sciences.

[61]  Robert Miller,et al.  Cortico-hippocampal interplay: Self-organizing phase-locked loops for indexing memory , 1989, Psychobiology.

[62]  K. Ikeda,et al.  Maxwell-Bloch Turbulence , 1989 .

[63]  M. Stryker.  Is grandmother an oscillation? , 1989, Nature.

[64]  K. Miller,et al.  Ocular dominance column development: analysis and simulation. , 1989, Science.

[65]  L. Ingber.  Very fast simulated re-annealing , 1989 .

[66]  T. Bullock,et al.  Lateral coherence of the electrocorticogram: a new measure of brain synchrony. , 1989, Electroencephalography and clinical neurophysiology.

[67]  Daniel J. Amit,et al.  Modeling brain function: the world of attractor neural networks, 1st Edition , 1989 .

[68]  W. Singer,et al.  Oscillatory responses in cat visual cortex exhibit inter-columnar synchronization which reflects global stimulus properties , 1989, Nature.

[69]  F Ventriglia.  Activity in cortical-like neural systems: short-range effects and attention phenomena. , 1990, Bulletin of mathematical biology.

[70]  K. Kaneko.  Clustering, coding, switching, hierarchical ordering, and control in a network of chaotic elements , 1990 .

[71]  W. Pitts,et al.  A Logical Calculus of the Ideas Immanent in Nervous Activity (1943) , 2021, Ideas That Created the Future.

[72]  Kaneko,et al.  Globally coupled chaos violates the law of large numbers but not the central-limit theorem. , 1990, Physical review letters.

[73]  Daniel J. Amit,et al.  Attractor neural networks with biological probe records , 1990 .

[74]  Paul L. Nunez,et al.  Multiple scales of statistical physics of the neocortex: Application to electroencephalography , 1990 .

[75]  Ingber,et al.  Statistical-mechanical aids to calculating term-structure models. , 1990, Physical review. A, Atomic, molecular, and optical physics.

[76]  Yong Yao,et al.  Model of biological pattern recognition with spatially chaotic dynamics , 1990, Neural Networks.

[77]  M. Stewart,et al.  Do septal neurons pace the hippocampal theta rhythm? , 1990, Trends in Neurosciences.

[78]  Towards a kinetic theory of some global brain activities. , 1990, Acta neurologica.

[79]  F. L. D. Silva,et al.  Basic mechanisms of cerebral rhythmic activities , 1990 .

[80]  James Theiler,et al.  Testing for nonlinearity in time series: the method of surrogate data , 1992 .

[81]  F. H. Lopes da Silva,et al.  Chaos or noise in EEG signals; dependence on state and brain site. , 1991, Electroencephalography and clinical neurophysiology.

[82]  Prof. Dr. Valentino Braitenberg,et al.  Anatomy of the Cortex , 1991, Studies of Brain Function.

[83]  Hermann Haken,et al.  Rhythms in Physiological Systems , 1991 .

[84]  D. Amit,et al.  Quantitative study of attractor neural networks retrieving at low spike rates: II. Low-rate retrieval in symmetric networks , 1991 .

[85]  Walter J. Freeman,et al.  Asymmetric sigmoid non-linearity in the rat olfactory system , 1991, Brain Research.

[86]  J. J. Wright,et al.  Radial coherence, wave velocity and damping of electrocortical waves. , 1991, Electroencephalography and clinical neurophysiology.

[87]  Ingber,et al.  Statistical mechanics of neocortical interactions: A scaling paradigm applied to electroencephalography. , 1991, Physical review. A, Atomic, molecular, and optical physics.

[88]  Arun V. Holden,et al.  Mathematical approaches to brain functioning diagnostics , 1991 .

[89]  Y. Miyashita,et al.  Neural organization for the long-term memory of paired associates , 1991, Nature.

[90]  Hans Liljenström.  Modeling the Dynamics of Olfactory Cortex Using Simplified Network Units and Realistic Architecture , 1991, Int. J. Neural Syst..

[91]  M Molnár,et al.  Low-dimensional chaos in event-related brain potentials. , 1992, The International journal of neuroscience.

[92]  T. Bullock,et al.  Induced Rhythms in the Brain , 1992, Brain Dynamics.

[93]  Stanislas Dehaene,et al.  Stabilization of complex input-output functions in neural clusters formed by synapse selection , 1992, Neural Networks.

[94]  K. Kaneko.  Mean field fluctuation of a network of chaotic elements: Remaining fluctuation and correlation in the large size limit , 1992 .

[95]  Ingber,et al.  Generic mesoscopic neural networks based on statistical mechanics of neocortical interactions. , 1992, Physical review. A, Atomic, molecular, and optical physics.

[96]  Mark Molnar,et al.  Application of chaos theory to biology and medicine , 1992, Integrative physiological and behavioral science : the official journal of the Pavlovian Society.

[97]  D. T. Kaplan,et al.  Direct test for determinism in a time series. , 1992, Physical review letters.

[98]  Walter J. Freeman,et al.  TUTORIAL ON NEUROBIOLOGY: FROM SINGLE NEURONS TO BRAIN CHAOS , 1992 .

[99]  J. Bower,et al.  Cortical oscillations and temporal interactions in a computer simulation of piriform cortex. , 1992, Journal of neurophysiology.

[100]  K. Oka,et al.  Long-term transformation of an inhibitory into an excitatory GABAergic synaptic response. , 1992, Proceedings of the National Academy of Sciences of the United States of America.

[101]  Robbie Case,et al.  The role of the frontal lobes in the regulation of cognitive development , 1992, Brain and Cognition.

[102]  Ichiro Tsuda,et al.  Dynamic link of memory--Chaotic memory map in nonequilibrium neural networks , 1992, Neural Networks.

[103]  H. Haken,et al.  PHASE TRANSITIONS IN THE HUMAN BRAIN: SPATIAL MODE DYNAMICS , 1992 .

[104]  M. Tovée,et al.  Oscillatory activity is not evident in the primate temporal visual cortex with static stimuli , 1992, Neuroreport.

[105]  L. Tsimring,et al.  The analysis of observed chaotic data in physical systems , 1993 .

[106]  L. Ingber.  Adaptive Simulated Annealing (ASA) , 1993 .

[107]  Ramesh Srinivasan,et al.  Implications of recording strategy for estimates of neocortical dynamics with electroencephalography. , 1993, Chaos.

[108]  Marvin Minsky,et al.  Allen Newell, Unified Theories of Cognition , 1993, Artif. Intell..

[109]  Robert A. M. Gregson,et al.  Cognitive load as a determinant of the dimensionality of the electroencephalogram: A replication study , 1993, Biological Psychology.

[110]  Daniel J. Amit,et al.  Conversion of Temporal Correlations Between Stimuli to Spatial Correlations Between Attractors , 1999, Neural Computation.

[111]  R. Llinás,et al.  Coherent 40-Hz oscillation characterizes dream state in humans. , 1993, Proceedings of the National Academy of Sciences of the United States of America.

[112]  Ichiro Tsuda,et al.  Can stochastic renewal of maps be a model for cerebral cortex , 1993 .

[113]  Albano,et al.  Filtered noise can mimic low-dimensional chaotic attractors. , 1993, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[114]  S. Bressler,et al.  Episodic multiregional cortical coherence at multiple frequencies during visual task performance , 1993, Nature.

[115]  E. Brazhnik,et al.  Acetylcholine, theta-rhythm and activity of hippocampal neurons in the rabbit—III. Cortical input , 1993, Neuroscience.

[116]  A. Aertsen,et al.  Response synchronization in the visual cortex , 1993, Current Opinion in Neurobiology.

[117]  R. Llinás,et al.  Human oscillatory brain activity near 40 Hz coexists with cognitive temporal binding. , 1994, Proceedings of the National Academy of Sciences of the United States of America.

[118]  Formation of rhythmic processes in the bioelectrical activity of the cerebral cortex , 1994 .

[119]  David Ruelle,et al.  Where Can One Hope to Profitably Apply the Ideas of Chaos , 1994 .

[120]  H. Liljenström,et al.  Regulating the nonlinear dynamics of olfactory cortex , 1994 .

[121]  James E. Skinner,et al.  The point correlation dimension: Performance with nonstationary surrogate data and noise , 1994, Integrative physiological and behavioral science : the official journal of the Pavlovian Society.

[122]  David T. J. Liley,et al.  A millimetric-scale simulation of electrocortical wave dynamics based on anatomical estimates of cortical synaptic density , 1994 .

[123]  W. Ditto,et al.  Controlling chaos in the brain , 1994, Nature.

[124]  James M. Bower,et al.  The Book of GENESIS , 1994, Springer New York.

[125]  Almut Schüz,et al.  Patchiness as a means to get a message across , 1994, Trends in Neurosciences.

[126]  Joel L. Davis,et al.  Large-Scale Neuronal Theories of the Brain , 1994 .

[127]  A Babloyantz,et al.  Computation with chaos: a paradigm for cortical activity. , 1994, Proceedings of the National Academy of Sciences of the United States of America.

[128]  T. Elbert,et al.  Oscillatory Event-Related Brain Dynamics , 1994, NATO ASI Series.

[129]  F Wilczek.  A call for a new physics. , 1994, Science.

[130]  F. Crick,et al.  The Astonishing Hypothesis: The Scientific Search for the Soul , 1994 .

[131]  Ingber,et al.  Statistical mechanics of neocortical interactions: Path-integral evolution of short-term memory. , 1994, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[132]  H. Swadlow.  Efferent neurons and suspected interneurons in motor cortex of the awake rabbit: axonal properties, sensory receptive fields, and subthreshold synaptic inputs. , 1994, Journal of neurophysiology.

[133]  J. E. Skinner,et al.  Chaos and physiology: deterministic chaos in excitable cell assemblies. , 1994, Physiological reviews.

[134]  D. Liley,et al.  Computer simulation of electrocortical activity at millimetric scale. , 1994, Electroencephalography and clinical neurophysiology.

[135]  Walter J. Freeman,et al.  Neural mechanisms underlying destabilization of cortex by sensory input , 1994 .

[136]  P. Nunez,et al.  A theoretical and experimental study of high resolution EEG based on surface Laplacians and cortical imaging. , 1994, Electroencephalography and clinical neurophysiology.

[137]  M. Molnár,et al.  On the origin of the P3 event-related potential component. , 1994, International journal of psychophysiology : official journal of the International Organization of Psychophysiology.

[138]  Z J Kowalik,et al.  Testing the determinism of EEG and MEG , 1994, Integrative physiological and behavioral science : the official journal of the Pavlovian Society.

[139]  W. Singer,et al.  Temporal Coding in the Brain , 1994, Research and Perspectives in Neurosciences.

[140]  James J. Wright,et al.  Intracortical connectivity of pyramidal and stellate cells: estimates of synaptic densities and coupling symmetry , 1994 .

[141]  David T. J. Liley.  Models of electrocortical dynamics. , 1995 .

[142]  George Ruppeiner,et al.  Riemannian geometry in thermodynamic fluctuation theory , 1995 .

[143]  W. Pritchard,et al.  Dimensional analysis of resting human EEG. II: Surrogate-data testing indicates nonlinearity but not low-dimensional chaos. , 1995, Psychophysiology.

[144]  D. Amit.  The Hebbian paradigm reintegrated: Local reverberations as internal representations , 1995, Behavioral and Brain Sciences.

[145]  W. Freeman.  Societies of Brains: A Study in the Neuroscience of Love and Hate. By W. J. Freeman. Erlbaum: Hillsdale, NJ. 1994. , 1997, Psychological Medicine.

[146]  Péter Érdi,et al.  Chaos and learning in the olfactory bulb , 1995, Int. J. Intell. Syst..

[147]  Hans Liljenström,et al.  Noise-enhanced performance in a cortical associative memory model , 1995, Int. J. Neural Syst..

[148]  T. Bullock,et al.  EEG coherence has structure in the millimeter domain: subdural and hippocampal recordings from epileptic patients. , 1995, Electroencephalography and clinical neurophysiology.

[149]  Ingber,et al.  Statistical mechanics of neocortical interactions: Constraints on 40-Hz models of short-term memory. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[150]  Robin Robertson,et al.  Chaos theory in Psychology and the Life Sciences , 1995 .

[151]  F. H. Lopes da Silva,et al.  Chaos or noise in EEG signals , 1995 .

[152]  T. Bullock,et al.  Temporal fluctuations in coherence of brain waves. , 1995, Proceedings of the National Academy of Sciences of the United States of America.

[153]  M. Hasselmo,et al.  Cholinergic modulation of cortical oscillatory dynamics. , 1995, Journal of neurophysiology.

[154]  W. Freeman,et al.  COMPARISON OF EEG TIME SERIES FROM RAT OLFACTORY SYSTEM WITH MODEL COMPOSED OF NONLINEAR COUPLED OSCILLATORS , 1995 .

[155]  G. Buzsáki,et al.  Temporal structure in spatially organized neuronal ensembles: a role for interneuronal networks , 1995, Current Opinion in Neurobiology.

[156]  R. Traub,et al.  Synchronized oscillations in interneuron networks driven by metabotropic glutamate receptor activation , 1995, Nature.

[157]  Colin G. Ellard,et al.  Context and consciousness , 1995, Behavioral and Brain Sciences.

[158]  P. Nunez,et al.  Neocortical Dynamics and Human EEG Rhythms , 1995 .

[159]  Walter J. Freeman,et al.  Chaos in the brain: Possible roles in biological intelligence , 1995, Int. J. Intell. Syst..

[160]  J E Lisman,et al.  Storage of 7 +/- 2 short-term memories in oscillatory subcycles , 1995, Science.

[161]  C. H. Bennett,et al.  Quantum Information and Computation , 1995 .

[162]  M Molnár,et al.  Correlation dimension changes accompanying the occurrence of the mismatch negativity and the P3 event-related potential component. , 1995, Electroencephalography and clinical neurophysiology.

[163]  Ingber,et al.  Statistical mechanics of neocortical interactions: High-resolution path-integral calculation of short-term memory. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[164]  David T. J. Liley,et al.  Simulation of electrocortical waves , 1995, Biological Cybernetics.

[165]  A Oliver,et al.  The emergence of hierarchical clustered representations in a Hebbian neural network model that simulates aspects of development in the neocortex. , 1996, Network.

[166]  Ramesh Srinivasan,et al.  Path-integral evolution of chaos embedded in noise: Duffing neocortical analog , 1996 .

[167]  Robert Miller,et al.  Axonal Conduction Time and Human Cerebral Laterality: A Psycological Theory , 1996 .

[168]  Lester Ingber,et al.  Statistical Mechanics of Nonlinear Nonequilibrium Financial Markets: Applications to Optimized Trading , 1996 .

[169]  Terrence J. Sejnowski,et al.  The Computational Brain , 1996, Artif. Intell..

[170]  Lester Ingber,et al.  Trading markets with canonical momenta and adaptive simulated annealing , 1996 .

[171]  Lester Ingber.  Canonical Momenta Indicators of Financial Markets and Neocortical Eeg , 1997 .