Fig. 38. Realistic connectivities are characterized by translationally invariant local connections and translationally variant global connections. The basic model for the study of the interplay of local and global interactions is the embedded two-point connection in a locally connected neural network as shown in the figure

Fig. 38. Realistic connectivities are characterized by translationally invariant local connections and translationally variant global connections. The basic model for the study of the interplay of local and global interactions is the embedded two-point connection in a locally connected neural network as shown in the figure connectivity identifies the basic toy model for the study of local and global interactions. The change in the connection topology destabilizes the initial stationary dynamics and the system undergoes a transition to a new stationary state via a Hopf bifurcation. Detailed bifurcation diagrams are given in (Jirsa & Kelso 2000) in which the spatiotemporal reorganization is characterized as a function of the length of the two point connection.

Minor changes in the location of the terminals or the system parameters, such as the homogeneous or heterogeneous transmission speeds, may result in qualitatively different global neural field dynamics. As an example, in Fig. 39 a stimulus is introduced in the neighborhood of a terminal of a two-point

Fig. 39. A neural field following Jirsa and Haken (1996) with an embedded two-point connection at x=10 and x=40 is established. In the neighborhood of x=10, a brief stimulus excites the neural sheet locally and the neural field reorganizes globally in a large scale transient wave which damps out after a sufficiently long time (not shown here)

Fig. 39. A neural field following Jirsa and Haken (1996) with an embedded two-point connection at x=10 and x=40 is established. In the neighborhood of x=10, a brief stimulus excites the neural sheet locally and the neural field reorganizes globally in a large scale transient wave which damps out after a sufficiently long time (not shown here)

connection (based at x=10 and x=40), then the excitation of the neural field travels through the continuous sheet, but also transmits a signal via the heterogeneous pathway. A transient wave dynamics is observed on the global system scale and damps out after a sufficiently long enough time. With no heterogeneous connection, only a local excitation at x=10 would have been observed. Similarly, with no heterogeneous connection and with two stimuli at terminal sites x=10 and x=40, only two local excitations would have been observed, but no large scale organization as observed in Fig. 39.

The neurosciences have historically leaned strongly towards empiricism - a tradition which continues today. However, mathematical formalisms of dynamical phenomena have provided extraordinary explanatory and unifying insights in the physical sciences. The emerging advances in computational neurosciences, particularly with respect to brain connectivity, suggest that they will also come to play an important role in the brain sciences. The cross-fertilization of dynamical systems theory (see also the Chapters by Campbell, Horowitz & Husain and Stephan & Friston), graph theory (Sporns & Tononi), basic physics (Ferree & Nunez), and methodological advances in neuroimag-ing (Darvas & Leahy, Fuchs) will hopefully underpin advances which do not merely reduce problems in neuroscience to problems already solved in other fields, but instead allow those properties of the brain that are unique to inform novel and specific discoveries. We see this blending of universality and specificity as absolutely crucial. Too much of the former will yield simplifications that lose what is required of a system in order to look (and function) like a brain. Conversely, too much specific detail yields volumes of descriptive data that adds little to our understanding of the underlying principles of brain function.

In this chapter, we have overviewed developments in the field of dynamical neural modeling across several scales of magnitude - from the microscopic conductance models of bifurcating neurons, (briefly) through systems of coupled chaotic oscillators at the mesoscopic scale to models of large scale neural networks whose behavior generates the electroencephalographic and neuroimag-ing data that is acquired non-invasively from human subjects. Evidence of computationally significant processes has been documented in data sets from across this spectrum of scales - i.e. from the single cell to the whole brain. An open and important question then is the relationship between activity at different temporal and spatial scales (Churchland and Sejnowski 1992). A possible answer could be that the macroscopic dynamics is an epiphenomenon -that is, a summed output of dynamics that can only truly be modeled at the neuronal level. However, this approach cannot be reconciled with the successes of large-scale models, which engage the brain at macroscopic scales only, to provide descriptive explanations of neuroscience data. That is, as discussed in

Sect. 4 of the present chapter, a mean field reduction of the present state of the system is able to predict its future states. This suggests that synchronizing processes are able to enslave many of the (small scale) degrees of freedom into dynamical structures at larger scales whose behavior is then - to some degree - determined by the state of the system at that scale. Whilst the large scale processes that are sustained by such processes inevitably influence the dynamics of the small scale units, it also remains possible that small scale events - such as critical sensory inputs - are able to rapidly influence the behavior of the system as a whole.

Whilst such considerations preclude a purely reductionist approach, an adequate explanatory framework remains elusive. The situation may be analogous to a heated magnet that it is close to the Curie temperature (above which it loses the ability to be magnetized): The magnetic fields are purely an outcome of the dipoles of spinning electrons. Yet the spinning electrons are also strongly influenced by the larger-scale magnetic fields. Below the Curie temperature, the fields are sufficiently strong to overcome stochastic fluctuations of individual spin directions. Above the Curie temperature the emergent fields are insufficient in strength to enslave the electron dipoles and the metal cannot hold a macroscopic field. However, at the Curie temperature, there is just a sufficient degree of coherence at any given scale to overcome the stochastic fluctuations at the next smaller scale. However, fluctuations at a small scale are able to transiently cascade to larger scales, a phenomena known as criticality and exhibit scale free fluctuations. Or perhaps even more attractive are the spin glass systems where - in addition to these processes - there exist disordered structures embedded in the system which preclude a perfectly ordered system even at low temperatures. Many of such spatiotemporal pattern formation phenomena and their underlying mechanisms have been understood in the framework of Synergetics, a field pioneered by Hermann Haken (1983, 1999).

Whilst such arguments have an attractive appeal, we should bear in mind our own warning that the brain is not just another complex physical system - such as a heated metal - even one with embedded impurities! There exist additional complexities that are surely important to brain function. One such critical difference is that there do exist structures across spatial and temporal scales prior to the emergence of dynamically driven scale-free (and scale-specific) fluctuations. Is it possible that the interaction between scale-specific processes across a hierarchy of scales is somehow optimal? Fusi et al. (2005) have shown how a hierarchy of synaptic processes - each with characteristic time scales - can interact in order to optimize memory retention (upgrading new memories) and storage (maintaining selected memory for long periods of time). Breakspear & Stam (2005) modeled the interaction between scale-free dynamics and multiscale spatial architectures by defining dynamical systems on different wavelet subspaces, and with cross-scale coupling between subspaces. This would potentially allow for a recursive relationship between small and large-scale dynamics.

Such observations hopefully reflect the challenge of fusing the universal with the specific as an emerging frontier in neuroscience research.

The authors wish to acknowledge helpful comments by SA Knock, PL Nunez, PA Robinson and E Tognoli and funding by ATIP (CNRS), Brain NRG JSMF22002082, NH&MRC, Australia and ARC Australia.

References

Abeles M (1991) Corticonics. Cambridge University Press

Abeles M, Bergman H, Margalit E, Vaadia E (1993) Spatiotemporal firing patterns in the frontal cortex of behaving monkeys. J. Neurophysiol.70, 1629-1638 Abbott LF, van Vreeswijk C (1993) Asynchronous states in a network of pulse-

coupled oscillators. Phys. Rev. E 48, 1482-1490 Abraham RH, Shaw CD (1988) Dynamics - The Geometry of Behavior. Part Four:

Bifurcation Behavior. Addison-Wesley: Redwood City. Afraimovich V, Verichev N, Rabinovich M (1986) Stochastic synchronization of oscillation in dissipative systems. Radiophysics and Quantum Electronics 29, 795-801.

Amari S (1977) Dynamics of pattern formation in lateral-inhibition type neural fields. Biol. Cybern. 27, 77-87 Amit DJ (1989) Modelling Brain Function. New York, Cambridge University Press Amit DJ, Brunel N (1997) Model of global spontaneous activity and local structured activity during delay periods in the cerebral cortex. Cerebral Cortex 7, 237-252

An der Heiden U (1980). Analysis of neural networks. In Lecture Notes in Biomath-

ematics (S Levin, ed), volume 35. Springer-Verlag, New York Arbib M, Erdi P (2000) Structure, Function, and Dynamics: An Integrated Approach to Neural Organization. Behavioral and Brain Sciences 23, 513-571 Ashwin P, Buescu, J, Stewart, I (1996) From attractor to chaotic saddle: A tale of transverse stability. Nonlinearity, 9: 703-737. Ashwin P, Terry J (2000) On riddling and weak attractors. Physica D, 142, 87-100. Baker GL, Gollub JP (1990) Chaotic Dynamics: An Introduction. Cambridge University Press

Barana Gy, GrĂ¶bler T, Erdi P (1988) Statistical model of the hippocampal CA3 region I. The single-cell module: bursting model of the pyramidal cell. Biol. Cybern. 79, 301-308

Beggs JM, Klukas J, Chen W (2007) Connectivity and dynamics in local cortical networks. This Volume. Beurle RL (1956) Properties of a mass of cells capable of regenerating pulses. Philos.

Trans. Soc. London Ser. A240, 55-94 Braitenberg V, Schuz A (1991) Anatomy of the cortex. Statistics and geometry. Springer, Berlin Heidelberg New York

Breakspear M, Terry J, Friston KJ (2003) Modulation of excitatory synaptic coupling facilitates synchronization and complex dynamics in a nonlinear model of neuronal dynamics Network: Computation in Neural Systems 14, 703-732 Breakspear M (2004) "Dynamic" connectivity in neural systems: Theoretical and empirical considerations. Neuroinformatics 4,1-23. Breakspear M, Stam KJ (2005) Dynamics of a neural system with a multiscale architecture. Phil. Trans. R. Soc. B 360, 1051-1074. Breakspear M, Roberts JA, Terry JR, Rodrigues S, Robinson PA (2006) A unifying explanation of generalized seizures via the bifurcation analysis of a dynamical brain model. Cerebral Cortex, doi:10.1093/cercor/bhj072. Bressler SL (1990) The gamma wave: a cortical information carrier? Trends in Neuroscience 13(5), 161-162 Bressler SL (1995) Large-scale cortical networks and cognition. Brain Res. Rev. 20, 288-304

Bressler SL (2002) Understanding cognition through large-scale cortical networks.

Curr. Dir. Psych. Sci. 11, 58-61 Bressler SL (2003) Cortical coordination dynamics and the disorganization syndrome in schizophrenia. Neuropsychpharmacology 28, 535-539 Bressler SL, Kelso JAS (2001) Cortical coordination dynamics and cognition. Trends in Cog. Sci. 5, 26-36

Bressler SL, Tognoli E (2006) International Journal of Psychophysiology (in press) Bressler SL, Mcintosh AR (2007) The role of neural context in large-scale neurocog-

nitive network operations. This Volume. Brunel N, Hakim V (1999) Fast global oscillations in networks of integrate-and-fire neurons with low firing rates. Neural Comput. 11, 1621-1671 Bullmore ET, Rabe-Hesketh S, Morris RG, Williams SC, Gregory L, Gray JA, Brammer MJ (1996) Functional magnetic resonance image analysis of a large-scale neurocognitive network. Neuroimage 4, 16-33 Campbell SA (2007) Time Delays in Neural Systems. This Volume. Cessac B, Samuelides M (2006) From Neuron to Neural Network Dynamics. To appear in Dynamical Neural Network. Models and Applications to Neural Computation. Springer Berlin Heidelberg New York Chu PH, Milton JG, Cowan JD (1994) Connectivity and the dynamics of integrate-

and-fire neural networks. Int. J. Bifur. Chaos 4, 237-217 Churchland P, Sejnowski TJ (1992) The Compuational Brain. MIT Press. New York. Collet P, Eckmann J (1980) Iterated maps on the interval as dynamical systems, Birkhauser.

Coombes S, Lord GJ, Owen MR (2003) Waves and bumps in neuronal networks with axo-dendritic synaptic interactions. Physica D, 178, 219-241 Coombes S (2005) Waves, bumps, and patterns in neural field theories, Biological

Cybernetics 93, 91-108 Crick F, Koch C ((1990) Towards a neurobiological theory of consciousness. Seminars in the Neurosciences 2, 263-275 Cvitanovic P (1984) Universality in chaos. Adam Hilger: Bristol. Dayan P, Abbott LF (2001) Theoretical Neuroscience. MIT Press Cambridge, Massachusetts

De Monte S, d'Ovidio F, Mosekilde E (2003) Coherent regimes of globally coupled dynamical systems. Phys. Rev. Let. 90, 054102

Dhamala M, Jirsa VK, Ding M (2004) Transitions to synchrony in coupled bursting neurons. Phys. Rev. Lett. 92: 028101. Eckmann J, Ruelle D (1985) Ergodic theory of chaos and strange attractors. Reviews of Modern Physics, 57: 617-656 Erlhagen W, Schoner G (2002) Dynamic field theory of movement preparation..

Psychological Review 109, 545-572 Ermentrout B (1998) Neural networks as spatio-temporal pattern-forming systems.

Rep. Prog. Phys. 61: 353-430. Feigenbaum MJ (1978) Quantitative universality for a class of nonlinear transformations. J. Stat. Phys., 19: 25-52. Ferree TC, Nunez PL (2007) Primer on electroencephalography for functional connectivity. This volume FitzHugh R (1961) Impulses and physiological states in theoretical models of nerve membrane. Biophys. J. 1, 445-466 Frank TD, Daffertshofer A, Beek PJ, Haken H (1999) Impacts of noise on a field theoretical model of the human brain. Physica D, 127, 233-249 Frank TD, Daffertshofer A, Peper CE, Beek PJ, Haken H (2000) Towards a comprehensive theory of brain activity: coupled oscillator systems under external forces. Physica D, 144, 62-86 Freeman WJ (1975) Mass action in the nervous system. Academic Press New York Freeman WJ, Skarda CA (1985) Spatial EEG patterns, nonlinear dynamics and perception: the neo-Sheringtonian view. Brain Res Rev10, 147-175 Freeman WJ (1987) Simulation of chaotic EEG patterns with a dynamic model of the olfactory system. Biological Cybernetics, 56, 139-150 Freeman WJ (1992) Tutorial on neurobiology: From single neurons to brain chaos.

Inter. Journ. Bif. Chaos 2, 451-482 Fuchs A, Jirsa VK, Kelso JA (2000) Theory of the relation between human brain activity (MEG) and hand movements. Neuroimage 11(5), 359-369 Fujisaka H, Yamada T (1983) Stability theory of synchronized motion in coupled-

oscillator system. Progress in Theoretical Physics, 69, 32-47. Fusi S, Drew PJ, Abbott LF (2005). Cascade models of synaptically stored memories.

Neuron. 45, 599-611. Gardiner CW (2004) Handbook of Stochastic Methods. Springer Berlin Heidelberg New York

Gerstner W (2000) Population Dynamics of Spiking Neurons: Fast Transients, Asynchronous States, and Locking. Neural Computation 12, 43-89 Gerstner W, Kistler WM (2002) Spiking neuron models: Single neurons, populations, plasticity. Cambridge University Press Gray CM, Singer W (1989) Stimulus-specific neuronal oscillations in orientation columns of cat visual cortex. Proc. Nat. Acad. Sci. 86, 1698-1702 Grebogi C, Ott E, Yorke JA (1982) Chaotic atractors in crisis. Phys. Rev. Lett. 48: 1507-1510.

Griffith JS (1963) A field theory of neural nets: I. Derivation of field equations. Bull.

Math. Biophys. 25, 111-120 Griffith JS (1965) A field theory of neural nets: II. Properties of the field equations.

Bull. Math. Biophys. 27, 187-195 GrĂ¶bler T, Barna Gy, Erdi P (1988) Statistical model of the hippocampal CA3 region II. The population frame work: model of rhythmic activity in the CA3 slice. Biol. Cybern. 79, 309-321

Grossberg S (1988) Nonlinear Neural Networks: Principles, Mechanisms, and Architectures. Neural Networks 1, 17-61 Guckenheimer, J. (1987) Limit sets of S-unimodal maps with zero entropy, Communications in Mathematical Physics, 110: 655-659. Guevara MG (2003). Dynamics of excitable cells. In: Nonlinear Dynamics in Physiology and Medicine (A Beuter, L Glass, MC Mackey and MS Titcombe, eds). Springer-Verlag, New York, pp. 87-121. Haken H (1983) Synergetics. An introduction. 3rd edition. Springer Berlin, Heidelberg, New York

Haken H (1999) Information and Self-Organization. 2nd edition. Springer Berlin,

Heidelberg, New York Hindmarsh JL, Rose RM (1984) A model of neuronal bursting using three coupled first order differential equations. Proc. R. Soc. London, Ser. B 221, 87 Hodgkin AL, Huxley AF (1952) A Quantitative Description of Membrane Current and its Application to Conduction and Excitation in Nerve/Journal of Physiology, 117: 500-544

Hopfield JJ (1982) Neural networks and physical systems with emergent collective computational abilities. Proc. Nat. Acad. Sci. 79, 2554-2558 Hopfield JJ (1984) Neurons with graded response have collective computational properties like those of two-state neurons. Proc. Nat. Acad. Sci. 81, 3088-3092 Horwitz B, Friston KJ, Taylor JG (2000) Neural modeling and functional brain imaging: an overview. Neural Networks 13, 829-846 Izhikevich E (2005) Dynamical systems in neuroscience: The geometry of excitability and bursting. MIT Press. Jirsa VK, Haken H (1996) Field theory of electromagnetic brain activity. Physical

Review Letters, 77: 960-963. Jirsa VK, Haken H (1997) A derivation of a macroscopic field theory of the brain from the quasi-microscopic neural dynamics. Physica D 99: 503-526. Jirsa VK, Fuchs A, Kelso JAS (1998) Connecting cortical and behavioral dynamics:

bimanual coordination. Neural Computation 10, 2019-2045 Jirsa VK, Kelso JAS. (2000) Spatiotemporal pattern formation in continuous systems with heterogeneous connection topologies. Phys. Rev. E 62, 6, 8462-8465

Jirsa VK, Jantzen KJ, Fuchs A, Kelso JAS (2002) Spatiotemporal forward solution of the EEG and MEG using network modeling. IEEE Transactions on Medical Imaging, 21, 5, 493-504 Jirsa VK (2004) Connectivity and dynamics of neural information processing. Neu-

roinformatics 2 (2), 183-204 Jirsa VK (2004b) Information processing in brain and behavior displayed in large-scale scalp topographies such as EEG and MEG. Inter. J. Bif. Chaos 14(2), 679-692

Kaneko K (1997) Dominance of Milnor attractors and noise-induced selection in a multiattractor system. Physical Review Letters, 78: 2736-2739 Kiss T, Erdi P (2002) Mesoscopic Neurodynamics. BioSystems 64, 119-126 Koch C (1999) Biophysics of Computation. Information processing in single neurons.

Oxford University Press Larter R, Speelman B and Worth R M (1999) A coupled ordinary differential equation lattice model for the simulation of epileptic seizures. Chaos, 9: 795-804.

Liley DTJ, Cadusch PJ, Dafilis MP (2002) A spatially continuous mean field theory of electrocortical activity. Network-Computation in Neural Systems, 13, 67-113. Lopes da Silva FH, Hoeks A, Smits H, Zetterberg LH (1974) Model of brain rhythmic activity: the alpha-rhythm of the thalamus. Kybernetik 15,27-37 Lopes da Silva FH, Blanes W, Kalitzin S, Parra J, Suffczynski P, Velis DN (2003) Dynamical diseases of brain systems: different routes to epileptic seizures Trans. Biomed. Eng. 50: 540-548. Lorenz, E (1963) Deterministic nonperiodic flow. Journal of Atmospheric Science, 20: 130-141.

Maistrenko Y, Maistrenko V, Popovich A, Mosekilde E (1998) Transverse instability and riddled basins in a system of two coupled logistic maps. Physical Review E, 57: 2713-2724.

Mallot HA, Brittinger R (1989) Towards a network theory of cortical areas. In: Cot-teril RMJ. (ed) Models of brain function. Cambridge University Press, 175-189 Mallot HA, Giannakopoulos F (1996) population networks: a large-scale framework for modelling cortical neural networks. Biological Cybernatics 75, 441-452 McCormick DA, Bal T (1997) Sleep and Arousal: Thalamocortical mechanisms.

Ann. Rev. Neuroscience, 20: 185-215 McCulloch WS, Pitts W (1943) A logical calculus of the ideas immanent in nervous activity. Bull. Math. Biophys. 5:115-33. McIntosh AR (2000) Towards a network theory of cognition. Neural Netw. 13, 861-876

Mesulam MM (1998) From sensation to cognition. Ann. Neurol. 28, 597-613 Milton JG (1996) Dynamics of small neural populations. American Mathematical Society

Milton JG, Chkhenkeli SA, Towle VL (2007) Brain Connectivity and the Spread of

Epileptic Seizures. This volume. Milnor J (1985) On the concept of attractor. Communications in Mathematical

Physics, 99: 177-195. Morris C, Lecar H (1981) Voltage oscillations in the barnacle giant muscle fiber.

Biophysics J., 35: 193-213 Mountcastle VB (1978) An organizing principle for cerebral function: the unit module and the distributed system. In: Edelman GM, Mountcastle VB (Eds) The Mindful Brain. MIT Press, Cambridge MA Mountcastle VB (1998) Perceptual Neuroscience: the cerebral cortex. Harvard University Press, Cambridge MA Nagumo J, Arimoto S, Yoshizawa S (1962) An active pulse transmission line simulating nerve axon. Proc IRE. 50: 2061-2070.

Nunez PL (1974) The brain wave equation: a model for the EEG. Mathematical

Biosciences 21: 279-297. Nunez PL (1995) Neocortical dynamics and human EEG rhythms, Oxford University Press

Nykamp DQ, Tranchina D (2001) A population density approach that facilitates large-scale modeling of neural networks: Extension to slow inhibitory synapses. Neural Computation 13, 511-546 Nykamp DQ, Tranchina D (2000) A population density approach that facilitates large-scale modeling of neural networks: analysis and an application to orientation tuning. Journal of Computational Neuroscience 8, 19-50

Ratliff F, Knight BW, Graham N (1969) On tuning and amplification by lateral inhibition. PNAS 3: 733-740. Robinson PA, Rennie CJ, Wright JJ (1997) Propagation and stability of waves of electrical activity in the cerebral cortex. Physical Review E, 56: 826-840. Robinson PA, Rennie CJ, Wright JJ, Bahramali H, Gordon E, Rowe DL (2001) Prediction of electroencephalographic spectra from neurophysiology. Physical Review E 63, 021903

Robinson PA, Rennie CJ, Rowe DL (2002) Dynamics of large-scale brain activity in normal arousal states and epileptic seizures. Physical Review E 65, 041924. Robinson PA, Rennie CJ, Rowe DL, O'Connor SC (2004) Hum Brain Mapp 25, 53-72

Robinson PA, Rennie CJ, Rowe DL, O'Connor SC, Gordon E (2005) Phil. Trans.

Roy. Soc. Ser. B 360, 1043 Rodriguez, S, Terry JR, Breakspear M (2006) On the genesis of spike-wave activity in a mean-field model of human corticothalamic dynamics. Physics Letters A 355, 352-357

Rosenblatt F (1958) The perceptron: a probabilistic model for information storage and organization in the brain, Psychol. Rev. 65: 386-408. Rulkov N, Sushchik M, Tsimring L, Abarbenel H (1995) Generalized synchronization of chaos in unidirectionally coupled chaotic systems. Physical Review E, 51: 980-994.

Sejnowski TJ, Rosenberg CR (1987) Parallel networks that learn to pronounce English. Complex Systems, 1: 145-168. Smalheiser NR (2000) Walter Pitts. Perspectives in Biology and Medicine. 43: 217-226.

Sporns O (2003) Complex Neural Dynamics. In: Coordination Dynamics: Issues and

Trends. Jirsa VK & Kelso JAS (eds.) Springer Berlin Sporns O, Tononi G (2002) Classes of Network connectivity and dynamics. Complexity 7, 28-38

Sporns O, Tononi G (2007) Structural determinants of functional brain dynamics. This Volume.

Strogatz SH (1994) Nonlinear dynamics and Chaos. Addison-Wesley: Reading, MA. Steyn-Ross ML, Steyn-Ross DA, Sleigh JW, Liley DTJ (1999) Theoretical electroencephalogram stationary spectrum for a white-noise-driven cortex: Evidence for a general anesthetic-induced phase transition. Phys. Rev. E 60, 7299-7311 Szentagothai J (1975) The 'module-concept' in cerebral cortex architecture. Brain Res. 95, 476-496

Tagamets MA, Horwitz B (1998) Integrating electrophysiological and anatomical experimental data to create a large-scale model that simulates a delayed match-to-sample human brain imaging study. Cereb. Cortex 8, 310-320 Treisman A (1996) The binding problem. Curr. Pin. Neurobiol. 6, 171-178 van Rotterdam A, Lopes da Silva FH, van den Ende J, Viergever MA, Hermans AJ (1982) A model of the spatio- temporal characteristics of the alpha rhythm. Bulletin of Mathematical Biology. 44: 283-305. Valdes PA, Jimenez JC, Riera J, Biscay R, Ozaki T (1999) Nonlinear EEG analysis on a neural mass model. Biol. Cybern. 81, 415-424 Ventriglia F (1974) Kinetic approach to neural system. Bull. Math. Biol. 36, 535-544 Ventriglia F (1978) Propagation of excitation in a model of neural system. Biol. Cybern. 30, 75-79

Von Stein A, Rappelsberger P, Sarnthein J, Petsche H (1999) Synchronization between temporal and parietal cortex during multimodal object processing in man. Cereb. Cortex 9, 137-150 Wilson HR (1973) Cooperative phenomena in a homogenous cortical tissue model. In: Haken H. (ed.) Synergetics - Cooperative Phenomena in Multi-compartment Systems. B. G. Teubner, Stuttgart Wilson HR and Cowan JD (1972) Excitatory and inhibitory interactions in localized populations of model neurons. Biophys. J. 12, 1-23. Wilson HR, Cowan JD (1973) A mathematical theory of the functional dynamics of cortical and thalamic nervous tissue. Kybernetic 13, 55-80 Wright JJ, Liley DTJ (1996) Dynamics of the brain at global and microscopic scales: Neural networks and the EEG. Behav. Brain. Sci. 19, 285

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