Fast Global Oscillations in Networks of Integrate-and-Fire Neurons with Low Firing Rates

Neural Computation

Volumn 11, Issue 7, 1999, Pages 1621-1671

  Brunel, Nicolas ^a   Hakim, Vincent ^a  

^a ECOLE NORMALE SUPÉRIEURE   (France)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHM; ARTICLE; ARTIFICIAL NEURAL NETWORK; BIOLOGICAL MODEL; COMPUTER SIMULATION; ELECTROPHYSIOLOGY; NERVE CELL; NONLINEAR SYSTEM; PHYSIOLOGY; STATISTICAL MODEL; SYNAPSE;

ALGORITHMS; COMPUTER SIMULATION; ELECTROPHYSIOLOGY; LINEAR MODELS; MODELS, NEUROLOGICAL; NEURAL NETWORKS (COMPUTER); NEURONS; NONLINEAR DYNAMICS; SYNAPSES;

EID: 0033210816     PISSN: 08997667     EISSN: None     Source Type: Journal    
DOI: 10.1162/089976699300016179     Document Type: Article

References (47)

1. Abbott, L. F., & van Vreeswijk, C. (1993). Asynchronous states in a network of pulse-coupled oscillators. Phys. Rev. E, 48, 1483.
2. Abeles, M. (1991). Corticonics. New York: Cambridge University Press.
3. Abramowitz, M., & Stegun, I. A. (1970). Tables of mathematical functions. New York: Dover.
4. Amit, D. J., & Brunel, N. (1997a). A model of global spontaneous activity and local delay activity during delay periods in the cerebral cortex. Cerebral Cortex, 7, 237.
5. Amit, D. J., & Brunel, N. (1997b). Dynamics of recurrent networks of spiking neurons before and after learning. Network, 8, 373.
6. Bragin, A., Jando, G., Nadasdy, Z., Hetke, J., Wise, K., & Buzsáki, G. (1995). Gamma (40-100 Hz) oscillation in the hippocampus of the behaving rat. J. Neurosci., 15, 47.
7. Braitenberg, V., & Schütz, A. (1991). Anatomy of cortex. Berlin: Springer-Verlag.
8. Bender, C. M., & Orszag, S. A. (1987). Advanced mathematical methods for scientists and engineers. New York: McGraw-Hill.
9. Buzsáki, G., & Chrobak, J. J. (1995). Temporal structure in spatially organized neuronal ensembles: A role for interneuronal networks. Current Opinion in Neurobiology, 5, 504.
10. Buzsáki, G., Horvath, Z., Urioste, R., Hetke, J., & Wise, K. (1992). High frequency network oscillation in the hippocampus. Science, 256, 1025.
11. Chandrasekhar, S. (1943). Stochastic problems in physics and astronomy. Rev. Mod. Phys., 15, 1.
12. Csicsvari, J., Hirase, H., Czurko, A., & Buzsáki, G. (1998). Reliability and state dependence of pyramidal cell-interneuron synapses in the hippocampus: An ensemble approach in the behaving rat. Neuron, 21, 179-189.
13. Delaney, K. R., Gelperin, A., Fee, M. S., Flores, J. A., Gervais, R., Tank, D. W., & Kleinfeld, D. (1994). Waves and stimulus-modulated dynamics in an oscillating olfactory network. Proc. Natl. Acad. Sci. USA, 91, 669-673.
14. Eckhorn, R., Frien, A., Bauer, R., Woelbern, T., & Kehr, H. (1993). High frequency (60-90 Hz) oscillations in primary visual cortex of awake monkey. NeuroReport, 4, 243-246.
15. Fisahn, A., Pike, F. G., Buhl, E. H., & Paulsen, O. (1998). Cholinergic induction of network oscillations at 40hz in the hippocampus in vitro. Nature, 394, 186-189.
16. Gardiner, C. W. (1983). Handbook of stochastic methods. Berlin: Springer-Verlag.
17. Gerstner, W. (1995). Time structure of the activity in neural network models. Phys. Rev. E, 51, 738-758.
18. Gerstner, W., van Hemmen, J. L., & Cowan, J. D. (1996). What matters in neuronal locking? Neural Computation, 8, 1653-1676.
19. Golomb, D., & Rinzel, J. (1994). Clustering in globally coupled inhibitory neurons. Physica D, 72, 259-282.
20. Gray, C. M. (1994). Synchronous oscillations in neuronal systems: Mechanisms and functions. J. Comput. Neurosci., 1, 11-38.
21. Gray, C. M., König, P., Engel, A. K., & Singer, W. (1989). Oscillatory responses in cat visual cortex exhibit inter-columnar synchronization which reflects global stimulus patterns. Nature, 338, 334.
22. Gray, C. M., & McCormick, D. A. (1996). Chattering cells: Superficial pyramidal neurons contributing to the generation of synchronous oscillations in the visual cortex. Science, 274, 109.
23. Hansel, D., Mato, G., & Meunier, C. (1995). Synchrony in excitatory neural networks. Neural Computation, 7, 307.
24. Hirsch, M. W., & Smale, S. (1974). Differential equations, dynamical systems and linear algebra. New York: Academic Press.
25. Kopell, N., & LeMasson, G. (1994). Rhythmogenesis, amplitude modulation, and multiplexing in a cortical architecture. Proc. Natl. Acad. Sci. USA, 91, 10586-10590.
26. Kreiter, A. K., & Singer, W. (1996). Stimulus-dependent synchronization of neuronal responses in the visual cortex of the awake macaque monkey. J. Neurosci., 26, 2381.
27. Laurent, G., & Davidowitz, H. (1994). Encoding of olfactory information with oscillating neural assemblies, Science, 265, 1872.
28. MacLeod, K. and Laurent, G. (1996). Distinct mechanisms for synchronization and temporal patterning of odor-encoding neural assemblies. Science, 274, 976-979.
29. Mirollo, R. E., & Strogatz, S. H. (1990). Synchronization of pulse-coupled biological oscillators. SIAM J. Appl. Math., 50, 1645.
30. Prechtl, J. C., Cohen, L. B., Pesaran, B., Mitra, P. P., & Kleinfeld, D. (1997). Visual stimuli induce waves of electrical activity in turtle cortex. Proc. Natl. Acad. Sci. USA, 94, 7621-7626.
31. Rappel, W. J., & Karma, A. (1996). Noise-induced coherence in neural networks. Phys. Rev. Lett., 77, 3256-3259.
32. Ritz, R., & Sejnowski, T. J. (1997). Synchronous oscillatory activity in sensory systems: New vistas on mechanisms. Current Opinion in Neurobiology, 7, 536-546.
33. Sakaguchi, H., Shinomoto, S., & Kuramoto, Y. (1988). Phase transitions and their bifurcation analysis in a large population of active rotators with mean-field coupling. Prog. Theor. Phys., 79, 600-607.
34. Singer, W., & Gray, C. M. (1995). Visual feature integration and the temporal correlation hypothesis. Ann. Rev. Neurosci., 18, 555.
35. Stopfer, M., Bhagavan, S., Smith, B. H., & Laurent, G. (1997). Impaired odour discrimination on desynchronization of odour-encoding neural assemblies. Nature, 390, 70-74.
36. Strogatz, S. H., & Mirollo, R. E. (1991). Stability of incoherence in a population of coupled oscillators. J. Stat. Phys., 63, 613-635.
37. Traub, R. D., Miles, R., & Wong, R. K. S. (1989). Model of the origin of rhythmic population oscillations in the hippocampal slice. Science, 243, 1319.
38. Traub, R. D., Whittington, M. A., Colling, S. B., Buzsáki, G., & Jefferys, J. G. R. (1996). Analysis of gamma rhythms in the rat hippocampus in vitro and in vivo. J. Physiol., 493, 471.
39. Treves, A. (1993). Mean-field analysis of neuronal spike dynamics. Network, 4, 259-284.
40. Tsodyks, M., & Sejnowski, T. (1995). Rapid state switching in balanced cortical network models. Network, 6, 111-124.
41. van Vreeswijk, C. (1996). Partial synchronization in populations of pulse-coupled oscillators. Phys. Rev. E, 54, 5522-5537.
42. van Vreeswijk, C., Abbott, L., & Ermentrout, G. B. (1994). When inhibition not excitation synchronizes neural firing. J. Comput. Neurosci., 1, 313.
43. van Vreeswijk, C., & Sompolinsky, H. (1996). Chaos in neuronal networks with balanced excitatory and inhibitory activity. Science, 274, 1724-1726.
44. Wang, X-J., & Buzsáki, G. (1996). Gamma oscillation by synaptic inhibition in a hippocampal interneuronal network model. J. Neurosci., 16, 6402.
45. Wang, X-J., Golomb, D., & Rinzel, J. (1995). Emergent spindle oscillations and intermittent burst firing in a thalamic model: Specific neuronal mechanisms. Proc. Natl. Acad. Sci. USA, 92, 5577-5581.
46. Whittington, M. A., Traub, R. D., & Jefferys, J. G. R. (1995). Synchronized oscillations in interneuron networks driven by metabotropic glutamate receptor activation. Nature, 373, 612.
47. Ylinen, A., Bragin, A., Nadasdy, Z., Jando, G., Szabo, I., Sik, A., & Buzsáki, G. (1995). Sharp-wave associated high frequency oscillation (200 Hz) in the intact hippocampus: Network and intracellular mechanisms. J. Neurosci., 15, 30.