Neuronal dynamics and brain connectivity

Understanding Complex Systems

Volumn 2007, Issue , 2007, Pages 3-64

  Breakspear, Michael ^a,b   Jirsa, Viktor K ^c,d  

^a UNIVERSITY OF NEW SOUTH WALES   (Australia)

^b UNIVERSITY OF SYDNEY   (Australia)

^c UMR6152 Mouvement and Perception   (France)

^d FLORIDA ATLANTIC UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 34548125774     PISSN: 18600832     EISSN: None     Source Type: Book Series    
DOI: 10.1007/978-3-540-71512-2_1     Document Type: Article

References (135)

1. Abeles M (1991) Corticonics. Cambridge University Press
2. Abeles M, Bergman H, Margalit E, Vaadia E (1993) Spatiotemporal firing patterns in the frontal cortex of behaving monkeys. J. Neurophysiol.70, 1629-1638
3. Abbott LF, van Vreeswijk C (1993) Asynchronous states in a network of pulsecoupled oscillators. Phys. Rev. E 48, 1482-1490
4. Abraham RH, Shaw CD (1988) Dynamics - The Geometry of Behavior. Part Four: Bifurcation Behavior. Addison-Wesley: Redwood City.
5. Afraimovich V, Verichev N, Rabinovich M (1986) Stochastic synchronization of oscillation in dissipative systems. Radiophysics and Quantum Electronics 29, 795-801.
6. Amari S (1977) Dynamics of pattern formation in lateral-inhibition type neural fields. Biol. Cybern. 27, 77-87
7. Amit DJ (1989) Modelling Brain Function. New York, Cambridge University Press
8. 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
9. An der Heiden U (1980). Analysis of neural networks. In Lecture Notes in Biomathematics (S Levin, ed), volume 35. Springer-Verlag, New York
10. Arbib M, Érdi P (2000) Structure, Function, and Dynamics: An Integrated Approach to Neural Organization. Behavioral and Brain Sciences 23, 513-571
11. Ashwin P, Buescu, J, Stewart, I (1996) From attractor to chaotic saddle: A tale of transverse stability. Nonlinearity, 9: 703-737.
12. Ashwin P, Terry J (2000) On riddling and weak attractors. Physica D, 142, 87-100.
13. Baker GL, Gollub JP (1990) Chaotic Dynamics: An Introduction. Cambridge University Press
14. Barana Gy, Gröbler T, Érdi 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
15. Beggs JM, Klukas J, Chen W (2007) Connectivity and dynamics in local cortical networks. This Volume.
16. Beurle RL (1956) Properties of a mass of cells capable of regenerating pulses. Philos. Trans. Soc. London Ser. A240, 55-94
17. Braitenberg V, Schüz A (1991) Anatomy of the cortex. Statistics and geometry. Springer, Berlin Heidelberg New York
18. 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
19. Breakspear M (2004) "Dynamic" connectivity in neural systems: Theoretical and empirical considerations. Neuroinformatics 4,1-23.
20. Breakspear M, Stam KJ (2005) Dynamics of a neural system with a multiscale architecture. Phil. Trans. R. Soc. B 360, 1051-1074.
21. 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.
22. Bressler SL (1990) The gamma wave: A cortical information carrier? Trends in Neuroscience 13(5), 161-162
23. Bressler SL (1995) Large-scale cortical networks and cognition. Brain Res. Rev. 20, 288-304
24. Bressler SL (2002) Understanding cognition through large-scale cortical networks. Curr. Dir. Psych. Sci. 11, 58-61
25. Bressler SL (2003) Cortical coordination dynamics and the disorganization syndrome in schizophrenia. Neuropsychpharmacology 28, 535-539
26. Bressler SL, Kelso JAS (2001) Cortical coordination dynamics and cognition. Trends in Cog. Sci. 5, 26-36
27. Bressler SL, Tognoli E (2006) International Journal of Psychophysiology (in press)
28. Bressler SL, McIntosh AR (2007) The role of neural context in large-scale neurocognitive network operations. This Volume.
29. Brunel N, Hakim V (1999) Fast global oscillations in networks of integrate-and-fire neurons with low firing rates. Neural Comput. 11, 1621-1671
30. 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
31. Campbell SA (2007) Time Delays in Neural Systems. This Volume.
32. 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
33. Chu PH, Milton JG, Cowan JD (1994) Connectivity and the dynamics of integrateand- fire neural networks. Int. J. Bifur. Chaos 4, 237-217
34. Churchland P, Sejnowski TJ (1992) The Compuational Brain. MIT Press. New York.
35. Collet P, Eckmann J (1980) Iterated maps on the interval as dynamical systems, Birkhauser.
36. Coombes S, Lord GJ, Owen MR (2003) Waves and bumps in neuronal networks with axo-dendritic synaptic interactions. Physica D, 178, 219-241
37. Coombes S (2005) Waves, bumps, and patterns in neural field theories, Biological Cybernetics 93, 91-108
38. Crick F, Koch C ((1990) Towards a neurobiological theory of consciousness. Seminars in the Neurosciences 2, 263-275
39. Cvitanovic P (1984) Universality in chaos. Adam Hilger: Bristol.
40. Dayan P, Abbott LF (2001) Theoretical Neuroscience. MIT Press Cambridge, Massachusetts
41. De Monte S, d'Ovidio F, Mosekilde E (2003) Coherent regimes of globally coupled dynamical systems. Phys. Rev. Let. 90, 054102
42. Dhamala M, Jirsa VK, Ding M (2004) Transitions to synchrony in coupled bursting neurons. Phys. Rev. Lett. 92: 028101.
43. Eckmann J, Ruelle D (1985) Ergodic theory of chaos and strange attractors. Reviews of Modern Physics, 57: 617-656
44. Erlhagen W, Schöner G (2002) Dynamic field theory of movement preparation. Psychological Review 109, 545-572
45. Ermentrout B (1998) Neural networks as spatio-temporal pattern-forming systems. Rep. Prog. Phys. 61: 353-430.
46. Feigenbaum MJ (1978) Quantitative universality for a class of nonlinear transformations. J. Stat. Phys., 19: 25-52.
47. Ferree TC, Nunez PL (2007) Primer on electroencephalography for functional connectivity. This volume
48. FitzHugh R (1961) Impulses and physiological states in theoretical models of nerve membrane. Biophys. J. 1, 445-466
49. 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
50. 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
51. Freeman WJ (1975) Mass action in the nervous system. Academic Press New York
52. Freeman WJ, Skarda CA (1985) Spatial EEG patterns, nonlinear dynamics and perception: The neo-Sheringtonian view. Brain Res Rev10, 147-175
53. Freeman WJ (1987) Simulation of chaotic EEG patterns with a dynamic model of the olfactory system. Biological Cybernetics, 56, 139-150
54. Freeman WJ (1992) Tutorial on neurobiology: From single neurons to brain chaos. Inter. Journ. Bif. Chaos 2, 451-482
55. Fuchs A, Jirsa VK, Kelso JA (2000) Theory of the relation between human brain activity (MEG) and hand movements. Neuroimage 11(5), 359-369
56. Fujisaka H, Yamada T (1983) Stability theory of synchronized motion in coupled-oscillator system. Progress in Theoretical Physics, 69, 32-47.
57. Fusi S, Drew PJ, Abbott LF (2005). Cascade models of synaptically stored memories. Neuron. 45, 599-611.
58. Gardiner CW (2004) Handbook of Stochastic Methods. Springer Berlin Heidelberg New York
59. Gerstner W (2000) Population Dynamics of Spiking Neurons: Fast Transients, Asynchronous States, and Locking. Neural Computation 12, 43-89
60. Gerstner W, Kistler WM (2002) Spiking neuron models: Single neurons, populations, plasticity. Cambridge University Press
61. Gray CM, Singer W (1989) Stimulus-specific neuronal oscillations in orientation columns of cat visual cortex. Proc. Nat. Acad. Sci. 86, 1698-1702
62. Grebogi C, Ott E, Yorke JA (1982) Chaotic atractors in crisis. Phys. Rev. Lett. 48: 1507-1510.
63. Griffith JS (1963) A field theory of neural nets: I. Derivation of field equations. Bull. Math. Biophys. 25, 111-120
64. Griffith JS (1965) A field theory of neural nets: II. Properties of the field equations. Bull. Math. Biophys. 27, 187-195
65. Gröbler T, Barna Gy, Érdi 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
66. Grossberg S (1988) Nonlinear Neural Networks: Principles, Mechanisms, and Architectures. Neural Networks 1, 17-61
67. Guckenheimer, J. (1987) Limit sets of S-unimodal maps with zero entropy, Communications in Mathematical Physics, 110: 655-659.
68. 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.
69. rd edition. Springer Berlin, Heidelberg, New York
70. nd edition. Springer Berlin, Heidelberg, New York
71. 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
72. 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
73. Hopfield JJ (1982) Neural networks and physical systems with emergent collective computational abilities. Proc. Nat. Acad. Sci. 79, 2554-2558
74. Hopfield JJ (1984) Neurons with graded response have collective computational properties like those of two-state neurons. Proc. Nat. Acad. Sci. 81, 3088-3092
75. Horwitz B, Friston KJ, Taylor JG (2000) Neural modeling and functional brain imaging: An overview. Neural Networks 13, 829-846
76. Izhikevich E (2005) Dynamical systems in neuroscience: The geometry of excitability and bursting. MIT Press.
77. Jirsa VK, Haken H (1996) Field theory of electromagnetic brain activity. Physical Review Letters, 77: 960-963.
78. 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.
79. Jirsa VK, Fuchs A, Kelso JAS (1998) Connecting cortical and behavioral dynamics: Bimanual coordination. Neural Computation 10, 2019-2045
80. Jirsa VK, Kelso JAS. (2000) Spatiotemporal pattern formation in continuous systems with heterogeneous connection topologies. Phys. Rev. E 62, 6, 8462-8465
81. 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
82. Jirsa VK (2004) Connectivity and dynamics of neural information processing. Neuroinformatics 2 (2), 183-204
83. Jirsa VK (2004b) Information processing in brain and behavior displayed in largescale scalp topographies such as EEG and MEG. Inter. J. Bif. Chaos 14(2), 679-692
84. Kaneko K (1997) Dominance of Milnor attractors and noise-induced selection in a multiattractor system. Physical Review Letters, 78: 2736-2739
85. Kiss T, Érdi P (2002) Mesoscopic Neurodynamics. BioSystems 64, 119-126 Koch C (1999) Biophysics of Computation. Information processing in single neurons. Oxford University Press
86. 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.
87. Liley DTJ, Cadusch PJ, Dafilis MP (2002) A spatially continuous mean field theory of electrocortical activity. Network-Computation in Neural Systems, 13, 67-113.
88. 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
89. 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.
90. Lorenz, E (1963) Deterministic nonperiodic flow. Journal of Atmospheric Science, 20: 130-141.
91. 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.
92. Mallot HA, Brittinger R (1989) Towards a network theory of cortical areas. In: Cotteril RMJ. (ed) Models of brain function. Cambridge University Press, 175-189
93. Mallot HA, Giannakopoulos F (1996) population networks: A large-scale framework for modelling cortical neural networks. Biological Cybernatics 75, 441-452
94. McCormick DA, Bal T (1997) Sleep and Arousal: Thalamocortical mechanisms. Ann. Rev. Neuroscience, 20: 185-215
95. McCulloch WS, Pitts W (1943) A logical calculus of the ideas immanent in nervous activity. Bull. Math. Biophys. 5:115-33.
96. McIntosh AR (2000) Towards a network theory of cognition. Neural Netw. 13, 861-876
97. Mesulam MM (1998) From sensation to cognition. Ann. Neurol. 28, 597-613
98. Milton JG (1996) Dynamics of small neural populations. American Mathematical Society
99. Milton JG, Chkhenkeli SA, Towle VL (2007) Brain Connectivity and the Spread of Epileptic Seizures. This volume.
100. Milnor J (1985) On the concept of attractor. Communications in Mathematical Physics, 99: 177-195.
101. Morris C, Lecar H (1981) Voltage oscillations in the barnacle giant muscle fiber. Biophysics J., 35: 193-213
102. 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
103. Mountcastle VB (1998) Perceptual Neuroscience: The cerebral cortex. Harvard University Press, Cambridge MA
104. Nagumo J, Arimoto S, Yoshizawa S (1962) An active pulse transmission line simulating nerve axon. Proc IRE. 50: 2061-2070.
105. Nunez PL (1974) The brain wave equation: A model for the EEG. Mathematical Biosciences 21: 279-297.
106. Nunez PL (1995) Neocortical dynamics and human EEG rhythms, Oxford University Press
107. 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
108. 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
109. Ratliff F, Knight BW, Graham N (1969) On tuning and amplification by lateral inhibition. PNAS 3: 733-740.
110. 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.
111. Robinson PA, Rennie CJ, Wright JJ, Bahramali H, Gordon E, Rowe DL (2001) Prediction of electroencephalographic spectra from neurophysiology. Physical Review E 63, 021903
112. 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.
113. Robinson PA, Rennie CJ, Rowe DL, O'Connor SC (2004) Hum Brain Mapp 25, 53-72
114. Robinson PA, Rennie CJ, Rowe DL, O'Connor SC, Gordon E (2005) Phil. Trans. Roy. Soc. Ser. B 360, 1043
115. 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
116. Rosenblatt F (1958) The perceptron: A probabilistic model for information storage and organization in the brain, Psychol. Rev. 65: 386-408.
117. Rulkov N, Sushchik M, Tsimring L, Abarbenel H (1995) Generalized synchronization of chaos in unidirectionally coupled chaotic systems. Physical Review E, 51: 980-994.
118. Sejnowski TJ, Rosenberg CR (1987) Parallel networks that learn to pronounce English. Complex Systems, 1: 145-168.
119. Smalheiser NR (2000) Walter Pitts. Perspectives in Biology and Medicine. 43: 217-226.
120. Sporns O (2003) Complex Neural Dynamics. In: Coordination Dynamics: Issues and Trends. Jirsa VK & Kelso JAS (eds.) Springer Berlin
121. Sporns O, Tononi G (2002) Classes of Network connectivity and dynamics. Complexity 7, 28-38
122. Sporns O, Tononi G (2007) Structural determinants of functional brain dynamics. This Volume.
123. Strogatz SH (1994) Nonlinear dynamics and Chaos. Addison-Wesley: Reading, MA.
124. 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
125. Szentagothai J (1975) The 'module-concept' in cerebral cortex architecture. Brain Res. 95, 476-496
126. Tagamets MA, Horwitz B (1998) Integrating electrophysiological and anatomical experimental data to create a large-scale model that simulates a delayed matchto- sample human brain imaging study. Cereb. Cortex 8, 310-320
127. 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.
128. Valdes PA, Jimenez JC, Riera J, Biscay R, Ozaki T (1999) Nonlinear EEG analysis on a neural mass model. Biol. Cybern. 81, 415-424
129. Ventriglia F (1974) Kinetic approach to neural system. Bull. Math. Biol. 36, 535-544
130. Ventriglia F (1978) Propagation of excitation in a model of neural system. Biol. Cybern. 30, 75-79
131. 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
132. 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
133. Wilson HR and Cowan JD (1972) Excitatory and inhibitory interactions in localized populations of model neurons. Biophys. J. 12, 1-23.
134. Wilson HR, Cowan JD (1973) A mathematical theory of the functional dynamics of cortical and thalamic nervous tissue. Kybernetic 13, 55-80
135. Wright JJ, Liley DTJ (1996) Dynamics of the brain at global and microscopic scales: Neural networks and the EEG. Behav. Brain. Sci. 19, 285