Population dynamics of spiking neurons: Fast transients, asynchronous states, and locking

Neural Computation

Volumn 12, Issue 1, 2000, Pages 43-89

  Gerstner, Wulfram ^a  

^a EPFL   (Switzerland)

Author keywords

[No Author keywords available]

Indexed keywords

ANIMAL; ARTICLE; ARTIFICIAL NEURAL NETWORK; BIOLOGICAL MODEL; BRAIN; NERVE CELL; NERVE CELL NETWORK; PHYSIOLOGY;

ANIMALS; BRAIN; MODELS, NEUROLOGICAL; NERVE NET; NEURAL NETWORKS (COMPUTER); NEURONS;

EID: 0033630628     PISSN: 08997667     EISSN: None     Source Type: Journal    
DOI: 10.1162/089976600300015899     Document Type: Article

References (67)

1. Abbott, L. F., & van Vreeswijk, C. (1993). Asynchronous states in a network of pulse-coupled oscillators. Phys. Rev. E, 48, 1483-1490.
2. Amari, S. (1974). A method of statistical neurodynamics. Kybernetik, 14, 201-215.
3. Bauer, H. U., & Pawelzik, K. (1993). Alternating oscillatory and stochastic dynamics in a model for a neuronal assembly. Physica D, 69, 380-393.
4. Brunel, N., & Hakim, V. (1999). Fast global oscillations in networks of integrate-and-fire neurons with low firing rates. Preprint submitted to Neural Computation.
5. Chow, C. C. (1998). Phase-locking in weakly heterogeneous neuronal networks. Physica D, 118, 343-370.
6. Cohen, M. A., & Grossberg, S. (1983). Absolute stability of global pattern formation and parallel memory storage by competitive neural networks. IEEE Trans. on Systems, Man, and Cybernetics, 13, 815-823.
7. Collins, J. J., Carson, C. C., Capela, A. C., & Imhoff, T. T. (1996). Aperiodic stochastic resonance. Physical Review E, 54, 5575-5584.
8. Connors, B. W., & Gutnick, M. J. (1990). Intrinsic firing patterns of diverse cortical neurons. Trends in Neurosci., 13, 99-104.
9. Cowan, J. D. (1968). Statistical mechanics of nervous nets. In E. R. Caianello (Ed.), Proceedings of the 1967 NATO Conference on Neural Networks. Berlin: Springer-Verlag.
10. Cox, D. R. (1962) Renewal theory. London: Methuen.
11. Cox, D. R., & Lewis, P. A. W. (1966). The statistical analysis of series of events. London: Methuen.
12. Eggert, J., & van Hemmen, J. L. Derivation of pool dynamics from microscopic neuronal models. In W. Gerstner et al. (Eds.), Artificial neural networks -ICANN'97 (pp. 109-114). Heidelberg: Springer-Verlag.
13. Ermentrout, G. B. (1981). N:M phase-locking in weakly coupled oscillators. J. Math. Biology, 12, 327-342.
14. Ernst, U., Pawelzik, K., & Geisel, T. (1994). Multiple phase clustering of globally coupled neurons with delay. In M. Marinaro & P. G. Morasso (Eds.), Proceedings of the ICANN'94 (pp. 1063-1065). Berlin: Springer-Verlag.
15. Feldman, J. L., & Cowan, J. D. (1975). Large-scale activity in neural nets I: Theory with application to motoneuron pool responses. Biol. Cybern., 17, 29-38.
16. Fetz, E. E., & Gustafsson, B. (1983). Relation between shapes of post-synaptic potentials and changes in firing probability of cat motoneurones. J. Physiol., 341, 387-410.
17. Gerstner, W. (1993). Kodierung und Signalübertragung in Neuronalen Systemen: Assoziative Netzwerke mit stochastisch feuernden Neuronen, Frankfurt/Main: Harri-Deutsch Verlag.
18. Gerstner, W. (1995). Time structure of the activity in neural network models. Phys. Rev. E, 51(1), 738-758.
19. Gerstner, W., & van Hemmen, J. L. (1992). Associative memory in a network of "spiking" neurons. Network, 3, 139-164.
20. Gerstner, W., & van Hemmen, J. L. (1993). Coherence and incoherence in a globally coupled ensemble of pulse emitting units. Phys. Rev. Lett., 71 (3), 312-315.
21. Gerstner, W., & van Hemmen, J. L. (1994). Coding and information processing in neural networks. In E. Domany, J. L. van Hemmen, & K. Schulten (Eds.), Models of neural networks II (pp. 1-93). New York: Springer-Verlag.
22. Gerstner, W., van Hemmen, J. L., & Cowan, J. D. (1996). What matters in neuronal locking. Neural Comput., 8, 1689-1712.
23. Golomb, D., Hansel, D., Shraiman, B., and Sompolinsky, H. (1992). Clustering in globally coupled phase oscillators. Phys. Rev. A, 45, 3516-3530.
24. Golomb, D., & Rinzel, J. (1994). Clustering in globally coupled inhibitory neurons. Physica D, 72, 259-282.
25. Gutkin, B., & Ermentrout, G. G. (1998). Dynamics of membrane excitability determine inter-spike interval variability: A link between spike generation mechanism and cortical spike train statistics. Neural Comput., 10, 1047-1065.
26. Hansel, D., Mato, G., & Meunier, C. (1995). Synchrony in excitatory neural networks. Neural Comput., 7, 307-337.
27. Hopfield, J. J. (1984). Neurons with graded response have computational properties like those of two-state neurons. Proc. Natl. Acad. Sci. USA, 81, 3088-3092.
28. Hopfield, J. J., & Herz, A. V. M. (1995). Rapid local synchronization of action potentials: Towards computation with coupled integrate-and-fire networks. Proc. Natl. Acad. Sci. USA, 92, 6655.
29. Horn, D., and Levanda, S. (1998). Fast temporal encoding and decoding with spiking neurons. Neural Comput., 10, 1705-1720.
30. Hubel, D. H., & Wiesel, T. N. (1962). Receptive fields, binocular interaction and functional architecture in the cat's visual cortex. J. Physiol. (London), 160, 106-154.
31. Kandel, E. C., & Schwartz, J. H. (1991). Principles of neural science. New York: Elsevier.
32. Kistler, W., Gerstner, W., & van Hemmen, J. L. (1997). Reduction of Hodgkin-Huxley equations to a single-variable threshold model. Neural Comput., 9, 1015-1045.
33. Knight, B. W. (1972a). Dynamics of encoding in a population of neurons J. Gen. Physiology, 59, 734-766.
34. Knight, B. W. (1972b). The relationship between the firing rate of a single neuron and the level of activity in a population of neurons J. Gen. Physiology, 59, 767-788.
35. Knox, C. K. (1974). Cross-correlation functions for a neuronal model Biophysical J., 14, 567-582.
36. Koch, C., Rapp, M., & Segev, I. (1996). A brief history of time constants. Cerebral Cortex, 6, 93-101.
37. Kuramoto, Y. (1975). Self-entrainment of a population of coupled nonlinear oscillators. In H. Araki (Ed.), International Symposium on Mathematical Problems in Theoretical Physics (pp. 420-422). Berlin: Springer-Verlag.
38. Kuramoto, Y. (1984). Chemical oscillations, waves, and turbulence. Berlin: Springer-Verlag.
39. Kuramoto, Y. (1991). Collective synchronization of pulse-coupled oscillators and excitable units Physica D, 50, 15-30.
40. Mirollo, R. E., & Strogatz, S. H. (1990). Synchronization of pulse coupled biological oscillators. SIAM J. Appl. Math., 50, 1645-1662.
41. Mountcastle, V. B. (1957). Modality and topographic properties of single neurons of cat's somatosensory cortex. J. Neurophysiol., 20, 408-434.
42. Nykamp, D., Tranchina, D., Shapley, R., & McLoughlin, D. (1998). A population density approach facilitates large-scale modeling of neural networks. To appear in Journal of Computational Neuroscience.
43. Perkel, D. H., Gerstein, G. L., & Moore, G. R (1967). Neuronal spike trains and stochastic point processes. (I) the single spike train. Biophys. J., 7, 391-418.
44. Pham, J., Pakdamen, K., Champagnat, J., & Vibert, J.-R. (1998). Activity in sparsely connected excitatory neural networks: Effect of connectivity. Neural Networks, 11, 415-438.
45. Pinto, D. J., Brumberg, J. C., Simons, D. J., & Ermentrout, G. B. (1996). A quantitative population model of whiskers barrels: Re-examining the Wilson-Cowan equations. J. Comput. Neurosci., 3, 247-264.
46. Plesser, H. E., & Gerstner, W. (1999). Noise in integrate-and-fire neurons: From stochastic input to escape rates. To appear in Neural Computation
47. Poliakov, A. V., Powers, R. K., & Binder, M. D. (1997). Functional identification of the input-output transforms of motoneurons in the rat and the cat J. Physiology, 504, 2:401-424.
48. Senn, W., Wyler, K., Streit, J., Larkum, M., Lüscher, H.-R., Mey, H., Müller, L., Steinhauser, D., Vogt, K., & Wannier, T. (1996). Dynamics of random neural network with synaptic depression. Neural Networks, 9, 575-588.
49. Somers, D., & Kopell, N. (1993). Rapid synchronization through fast threshold modulation. Biol. Cybern., 68, 393-407.
50. Spiridon, M., Chow, C. C., & Gerstner, W. (1998). Frequency spectrum of coupled stochastic neurons with refractoriness. In L. Niklasson et al. (Eds.), ICANN'98 (pp. 337-342). Berlin: Springer-Verlag.
51. Stein, R. B. (1967). Some models of neuronal variability. Biophys. J., 7, 37-68.
52. Stevens, C. F., & Zador, A. (1998). Novel integrate-and-fire-like model of repetitive firing in cortical neurons. In Proceedings of the Fifth Joint Symposion on Neural Computation, University of California at San Diego.
53. Strogatz, S. H., & Mirollo, R. E. (1991). Stability of incoherence in a population of coupled oscillators. J. Stat. Phys., 63, 613-635.
54. Terman, D., & Wang, D. (1995). Global competition and local cooperation in a network of neural oscillators. Physica D, 81, 148-176.
55. Thorpe, S., Fize, D., & Marlot, C. (1996). Speed of processing in the human visual system. Nature, 381, 520-522.
56. Treves, A. (1992). Local neocortical processing: A time for recognition, Int. J. Neural Systems, 3(Supp.), 115-119.
57. Treves, A. (1993). Mean-field analysis of neuronal spike dynamics. Network, 4, 259-284.
58. Treves, A., Rolls, E. T., & Simmen, M. (1997). Time for retrieval in recurrent associative memories. Physica D, 107, 392-400.
59. Tsodyks, M., Mitkov, I., & Sompolinsky, H. (1993). Patterns of synchrony in inhomogeneous networks of oscillators with pulse interaction. Phys. Rev. Lett., 71, 1281-1283.
60. Tsodyks, M. V., & Sejnowski, T. (1995). Rapid state switching in balanced cortical networks. Network, 6, 111-124.
61. Tuckwell, H. C. (1988). Introduction to theoretic neurobiology. Cambridge: Cambridge University Press.
62. Tuckwell, H. C. (1989). Stochastic processes in the neurosciences. Philadelphia: SIAM.
63. van Vreeswijk, C., Abbott, L. E., & Ermentrout, G. B. (1994). When inhibition not excitation synchronizes neural firing. Journal of Computational Neuroscience, 1, 313-321.
64. van Vreeswijk, C., & Sompolinsky, H. (1996). Chaos in neuronal networks with balanced excitatory and inhibitory activity. Science, 274, 1724-1726.
65. Wilson, H. R., & Cowan, J. D. (1972). Excitatory and inhibitory interactions in localized populations of model neurons. Biophysical J., 12, 1-24.
66. Wilson, H. R., & Cowan, J. D. (1973). A mathematical theory of the functional dynamics of cortical and thalamic nervous tissue. Kybernetik, 13, 55-80.
67. Winfree, A. T. (1980). The geometry of biological time. Berlin: Springer-Verlag.