Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Introduction
Goal Epileptic Seizures
Babloyantz, A., Strange attractors in the dynamics of brain activity. In: Complex systems — operational approaches. Haken, H. (ed.), Springer, Berlin 1985
Friedrich, R., Uhl, C.: Synergetic analysis of human electro-encephalograms: Petit-mal epilepsy. In: Evolution of dynamical structures in complex systems, R. Friedrich, A. Wunderlin (eds.), Springer, Berlin 1992
Binding Problem
Singer, W. (1999): Time as coding space? Curr. Opin. Neurobiol. 9, 189–194
Singer, W. (1999): Neuronal synchrony: a versatile code for the definition of relations? Neuron 24, 49–65
Singer, W., Gray, C.M. (1995): Visual feature integration and the temporal correlation hypothesis. Ann. Rev. Neurosci. 18, 555–586
Gray, C.M. (1999): The temporal correlation hypothesis: still alive and well. Neuron 24, 31–47
Wakefield, J. (2001): A mind for consciousness, Sci. American 285, 26–27
Recent work on Parkinsonian tremor
Tass, P., Phase resetting in medicine and biology — stochastic modelling and data analysis. Springer, Berlin 1999
Tass, P., Rosenblum, M.G., Weule, J., Kurths, J., Pikovsky, A.S., Volkmann, J., Schnitzler, A., Freund, H.J. (1998): Detection of n: m phase locking from noisy data: Application to magnetoencephalography. Phys. Rev. Lett. 81, 3291–3294
Brain: Structure and Functioning. A Brief Reminder
Adelman, G., Smith, B.H. (eds.), Elsevier’s encyclopedia of neuro-science, Elsevier Science, Amsterdam 1999
Arbib, M.A. (ed.), The handbook of brain theory and neural networks. MIT Press, Cambridge 2000
Bonhoeffer, T., Grinvald, A. (1996): Optical imaging based on intrinsic signals: The methodology. In: Toga, A., Masiotta, J.C. (eds.), Brain mapping: The methods. Academic Press, San Diego, CA., 55–97
Grinvald, A., Lieke, E., Frostig, R.D., Gilbert, C.D., Wiesel, T.N. (1986): Functional architecture of cortex revealed by optical imaging of intrinsic signals. Nature 324, 361–364
Network Models
Bresloff, P.C., Coombes, S. (1998): Phys. Rev. Lett. 81, 2168, 2384
Ernst, U., Pawelzik, K., Geisel, T. (1995): Synchronization induced by temporal delays in pulse-coupled oscillators. Phys. Rev. Lett. 74, 1570
Lighthouse model
Haken, H. (2000): Phase locking in the lighthouse model of a neural net with several delay times. In: Robnik, M., Aizawa, Y., Hasegawa, H., Kuramoto, Y. (eds.). Progr. of Theor. Physics, Supplement 139, 96–111
Haken, H., Associative memory of a pulse-coupled noisy neural network with delays: The lighthouse model. Proceedings of traffic and granular flow, Springer, Berlin 2000
Haken, H., Laser theory. Encyclopedia of physics XXV/2c, 2nd ed., Springer, Berlin 1984
Jirsa, V.K., Haken, H. (1996): Field theory of electromagnetic brain activity, Phys. Rev. Lett. 77, 960–963; (1996): Derivation of a field equation of brain activity, Journal of Biol. Physics 22, 101–112
Kelso, J.A.S. (1990): Phase transitions: Foundations of behavior. In: Haken, H., Stadler, M. (eds.), Synergetics of cognition, 249–295, Springer, Berlin
Kelso, J.A.S., Dynamic patterns: The self-organization of brain and behavior, MIT Press, Boston 1995
Kuramoto, Y., Chemical oscillations, waves, and turbulence, Springer, Berlin 1984
Kuramoto, Y., Nishikawa, I. (1987): J.Stat. Phys. 49, 569
Kuramoto, Y. (1991): Physica D 50, 15
Mirollo, R.E., Strogatz, S.H. (1990): Synchronization of pulse-coupled biological oscillators. SIAM J. Appl. Math. 50, 1645–1662
Nunez, P.L. (1974): The brain wave equation: A model for the EEG, Mathematical Biosciences 21, 279–297
Nunez, P.L., Electric fields of the brain, Oxford University Press 1981
Nunez, P.L., Neocortical dynamics and human EEG rhythms, Oxford University Press 1995
Peskin, C.S. (1975): Mathematical aspects of heart physiology, Courant Institute of Mathematical Sciences, New York University, New York, 268–278
For reviews on synchronization mechanisms in the brain cf.
Strogatz, S.M. (2000): From Kuramoto to Crawford: exploring the onset of synchronization in populations of coupled oscillators, Physica D 143
Sturz, A.K., König, P. (2001): Mechanisms for synchronization of neuronal activity, Biol. Cybern. 84, 153
Viterbi, A.J., Principles of coherent communication, McGraw Hill, New York 1966
Wilson, H.R. and Cowan, J.D. (1972): Excitatory and inhibitory interactions in localized populations of model neurons, Biophysical Journal, 12, 1–24
Winfree, A.T. (1967): J. Theor. Biol. 16, 15
Winfree, A.T., The Geometry of biological time, Springer, Berlin; 2nd ed. to be published 2001
In the context of our book, the contribution by Freeman is of particular interest
Freeman, W.J. (2000): Characteristics of the synchronization of brain activity imposed by finite conduction velocities of axons, Int. J. Bifurcation and Chaos 10, 2307–2322
Rights and permissions
Copyright information
© 2007 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
(2007). Introduction. In: Brain Dynamics. Springer Series in Synergetics. Springer, Berlin, Heidelberg . https://doi.org/10.1007/978-3-540-46284-2_1
Download citation
DOI: https://doi.org/10.1007/978-3-540-46284-2_1
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-46282-8
Online ISBN: 978-3-540-46284-2
eBook Packages: Springer Book Archive