Dynamics of neural networks

Principles of Neural Coding

Volumn , Issue , 2013, Pages 489-512

  Brunel, Nicolas ^a  

^a UNIVERSITY OF CHICAGO   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84896963421     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1201/b14756     Document Type: Chapter

References (118)

1. Abbott, L. F. and C. van Vreeswijk. 1993. Asynchronous states in a network of pulse-coupled oscillators. Phys Rev E 48, 1483-1490.
2. Amari, S. 1977. Dynamics of pattern formation in lateral-inhibition type neural fields. Biol Cybern 27, 77-87.
3. Amit, D. J. and N. Brunel. 1997a. Dynamics of a recurrent network of spiking neurons before and following learning. Network 8, 373-404.
4. Amit, D. J. and N. Brunel. 1997b. Model of global spontaneous activity and local structured activity during delay periods in the cerebral cortex. Cerebral Cortex 7, 237-252.
5. Amit, D. J. and M. V. Tsodyks. 1991. Quantitative study of attractor neural network retrieving at low spike rates I: Substrate-spikes, rates and neuronal gain. Network 2, 259-274.
6. Badel, L., S. Lefort, T. K. Berger, C. C. Petersen, W. Gerstner, and M. J. Richardson. 2008a. Extracting non-linear integrate-and-fire models from experimental data using dynamic I-V curves. Biol Cybern 99, 361-370.
7. Badel, L., S. Lefort, R. Brette, C. C. Petersen, W. Gerstner, and M. J. Richardson. 2008b. Dynamic I-V curves are reliable predictors of naturalistic pyramidal-neuron voltage traces. J Neurophysiol 99, 656-666.
8. Banerjee, A. 2006. On the sensitive dependence on initial conditions of the dynamics of networks of spiking neurons. J Comput Neurosci 20, 321-348.
9. Belitski, A., A. Gretton, C. Magri, Y. Murayama, M. A. Montemurro, N. K. Logothetis, and S. Panzeri. 2008. Low-frequency local field potentials and spikes in primary visual cortex convey independent visual information. J Neurosci 28, 5696-5709.
10. Ben-Yishai, R., D. Hansel, and H. Sompolinsky. 1997. Traveling waves and the processing of weakly tuned inputs in a cortical network module. J Comput Neurosci 4, 57-77.
11. Ben-Yishai, R., R. Lev Bar-Or, and H. Sompolinsky. 1995. Theory of orientation tuning in visual cortex. Proc Natl Acad Sci USA 92, 3844-3848.
12. Beurle, R. L. 1956. Properties of a mass of cells capable of regenerating pulses. Philos Trans Roy Soc London B 240, 5594.
13. Binzegger, T., R. J. Douglas, and K. A. Martin. 2004. A quantitative map of the circuit of cat primary visual cortex. J Neurosci 24, 8441-8453.
14. Bragin, A., G. Jando, Z. Nadasdy, J. Hetke, K. Wise, and G. Buzsáki. 1995. Gamma (40-100 Hz) oscillation in the hippocampus of the behaving rat. J Neurosci 15, 47-60.
15. Brette, R. and W. Gerstner. 2005. Adaptive exponential integrate-and-fire model as an effective description of neuronal activity. J Neurophysiol 94, 3637-3642.
16. Brette, R., M. Rudolph, T. Carnevale, M. Hines, D. Beeman, J. M. Bower, M. Diesmann et al. 2007. Simulation of networks of spiking neurons: A review of tools and strategies. J Comput Neurosci 23, 349-398.
17. Brunel, N. 2000. Dynamics of sparsely connected networks of excitatory and inhibitory spiking neurons. J Comput Neurosci 8, 183-208.
18. Brunel, N. 2009. Modeling point neurons: From Hodgkin-Huxley to integrate-and-fire. In E. D. Schutter (Ed.), Computational Modeling Methods for Neuroscientists. MIT Press, Cambridge, MA.
19. Brunel, N., F. Chance, N. Fourcaud, and L. Abbott. 2001. Effects of synaptic noise and filtering on the frequency response of spiking neurons. Phys Rev Lett 86, 2186-2189.
20. Brunel, N. and V. Hakim. 1999. Fast global oscillations in networks of integrate-and-fire neurons with low firing rates. Neural Comp 11, 1621-1671.
21. Brunel, N. and V. Hakim. 2009. Neuronal network dynamics. In R. A. Meyers (Ed.), Encyclopedia of Complexity and Systems Science. Springer. New York, NY.
22. Brunel, N. and D. Hansel. 2006. How noise affects the synchronization properties of networks of inhibitory neurons. Neural Comp 18, 1066-1110.
23. Brunel, N. and M. C. van Rossum. 2007. Lapicque’s 1907 paper: From frogs to integrate-and-fire. Biol Cybern 97, 337-339.
24. Brunel, N. and X.-J. Wang. 2003. What determines the frequency of fast network oscillations with irregular neural discharges? J Neurophysiol 90, 415-430.
25. Camperi, M. and X.-J. Wang. 1998. A model of visuospatial short-term memory in prefrontal cortex: Recurrent network and cellular bistability. J Comput Neurosci 5, 383-405.
26. Compte, A., C. Constantinidis, J. Tegnér, S. Raghavachari, M. Chafee, P. S. Goldman-Rakic, and X.-J. Wang. 2003. Temporally irregular mnemonic persistent activity in prefrontal neurons of monkeys during a delayed response task. J Neurophysiol 90, 3441-3454.
27. Csicsvari, J., H. Hirase, A. Czurko, A. Mamiya, and G. Buzsáki. 1999. Fast network oscillations in the hippocampal CA1 region of the behaving rat. J Neurosci 19, RC20.
28. Csicsvari, J., B. Jamieson, K. D. Wise, and G. Buzsaki. 2003. Mechanisms of gamma oscillations in the hippocampus of the behaving rat. Neuron 37, 311-322.
29. Dayan, P. and L. Abbott. 2001. Theoretical Neuroscience. MIT Press, Cambridge.
30. de la Rocha, J., B. Doiron, E. Shea-Brown, K. Josic, and A. Reyes. 2007. Correlation between neural spike trains increases with firing rate. Nature 448, 802-806.
31. de Solages, C., G. Szapiro, N. Brunel, V. Hakim, P. Isope, P. Buisseret, C. Rousseau, B. Barbour, and C. Lena. 2008. High-frequency organization and synchrony of activity in the Purkinje cell layer of the cerebellum. Neuron 58, 775-788.
32. Deco, G., V. K. Jirsa, and A. R. McIntosh. 2011. Emerging concepts for the dynamical organization of resting-state activity in the brain. Nat Rev Neurosci 12, 43-56.
33. Deco, G., V. K. Jirsa, P. A. Robinson, M. Breakspear, and K. Friston. 2008. The dynamic brain: From spiking neurons to neural masses and cortical fields. PLoS Comput Biol 4, e1000092.
34. Derrida, B., E. Gardner, and A. Zippelius. 1987. An exactly solvable asymmetric neural network model. Europhys Lett 4, 167-173.
35. Doiron, B., B. Lindner, A. Longtin, L. Maler, and J. Bastian. 2004. Oscillatory activity in electrosensory neurons increases with the spatial correlation of the stochastic input stimulus. Phys Rev Lett 93, 048101.
36. Ecker, A. S., P. Berens, G. A. Keliris, M. Bethge, N. K. Logothetis, and A. S. Tolias. 2010. Decorrelated neuronal firing in cortical microcircuits. Science 327, 584-587.
37. Ermentrout, G. B. 1994. Reduction of conductance based models with slow synapses to neural nets. Neural Comput 6, 679-695.
38. Ermentrout, G. B. 1996. Type I membranes, phase resetting curves, and synchrony. Neural Comput 8, 979-1001.
39. Ermentrout, G. B. 1998. Neural networks as spatio-temporal pattern-forming systems. Rep Prog Phys 61, 353-430.
40. Ermentrout, G. B. and N. Kopell. 1986. Parabolic bursting in an excitable system coupled with a slow oscillation. SIAM J Appl Math 46, 233-253.
41. Fourcaud N. and N. Brunel. 2002. Dynamics of the firing probability of noisy integrate-and-fire neurons. Neural Comput 14(9), 2057-2110.
42. Fourcaud-Trocmé, N., D. Hansel, C. van Vreeswijk, and N. Brunel. 2003. How spike generation mechanisms determine the neuronal response to fluctuating inputs. J Neurosci 23, 11628-11640.
43. Fuhrmann, G., H. Markram, and M. Tsodyks. 2002. Spike frequency adaptation and neocortical rhythms. J Neurophysiol 88, 761-770.
44. Geisler, C., N. Brunel, and X.-J. Wang. 2005. Contributions of intrinsic membrane dynamics to fast network oscillations with irregular neuronal discharges. J Neurophysiol 94, 4344-4361.
45. Gieselmann, M. A. and A. Thiele. 2008. Comparison of spatial integration and surround suppression characteristics in spiking activity and the local field potential in macaque V1. Eur J Neurosci 28, 447-459.
46. Griffith, J. S. 1963. A field theory of neural nets: I: Derivation of field equations. Bull Math Biophys 25, 111-120.
47. Griffith, J. S. 1965. A field theory of neural nets: Ii: Properties of field equations. Bull Math Biophys 27, 187-195.
48. Griffith, J. S. and G. Horn. 1966. An analysis of spontaneous impulse activity of units in the striate cortex of unrestrained cats. J Physiol (Lond) 186, 516-534.
49. Gutkin, B. and G. B. Ermentrout. 1998. Dynamics of membrane excitability determine interspike interval variability: A link between spike generation mechanisms and cortical spike train statistics. Neural Comp 10, 1047-1065.
50. Hansel, D. and H. Sompolinsky. 1998. Modeling feature selectivity in local cortical circuits. In C. Koch and I. Segev (Eds.), Methods in Neuronal Modeling (2nd ed.)., pp. 499-567. MIT Press, Cambridge, MA.
51. Henrie, J. A. and R. Shapley. 2005. LFP power spectra in V1 cortex: The graded effect of stimulus contrast. J Neurophysiol 94, 479-490.
52. Holmgren, C., T. Harkany, B. Svennenfors, and Y. Zilberter. 2003. Pyramidal cell communication within local networks in layer 2/3 of rat neocortex. J Physiol 551, 139-153.
53. Hromadka, T., M. R. Deweese, and A. M. Zador. 2008. Sparse representation of sounds in the unanesthetized auditory cortex. PLoS Biol 6, e16.
54. Izhikevich, E. M. 2001. Resonate-and-fire neurons. Neural Networks 14, 883-894.
55. Izhikevich, E. M. 2003. Simple model of spiking neurons. IEEE Trans Neural Networks 14, 1569-1572.
56. Jahnke, S., R. Memmesheimer, and M. Timme. 2008. Stable irregular dynamics in complex neural networks. Phys Rev Lett 100, 048102.
57. Jahnke, S., R. M. Memmesheimer, and M. Timme. 2009. How chaotic is the balanced state? Front Comput Neurosci 3, 13.
58. Jahr, C. E. and C. F. Stevens. 1990. Voltage dependence of NMDA-activated macroscopic conductances predicted by single-channel kinetics. J Neurosci 10, 3178-3182.
59. Klausberger, T. and P. Somogyi. 2008. Neuronal diversity and temporal dynamics: The unity of hippocampal circuit operations. Science 321, 53-57.
60. Knight, B. W. 1972. Dynamics of encoding in a population of neurons. J Gen Physiol 59, 734-766.
61. Koch, K. W. and J. M. Fuster. 1989. Unit activity in monkey parietal cortex related to haptic perception and temporary memory. Exp Brain Res.76, 292-306.
62. Kreiter, A. K. and W. Singer. 1996. Stimulus dependent synchronization of neuronal responses in the visual cortex of the awake macaque monkey. J Neurosci 16, 2381-.
63. Kumar, A., S. Schrader, A. Aertsen, and S. Rotter. 2008. The high-conductance state of cortical networks. Neural Comput 20, 1-43.
64. Lapicque, L. 1907. Recherches quantitatives sur l’excitabilité électrique des nerfs traitée comme une polarisation. J Physiol Pathol Gen 9, 620-635.
65. Latham, P. E., B. J. Richmond, P. G. Nelson, and S. Nirenberg. 2000. Intrinsic dynamics in neuronal networks. I. Theory. J Neurophysiol 83, 808.
66. Ledoux, E. and N. Brunel. 2011. Dynamics of networks of excitatory and inhibitory neurons in response to time-dependent inputs. Front Comput Neurosci 5, 25.
67. Lindner, B., B. Doiron, and A. Longtin. 2005. Theory of oscillatory firing induced by spatially correlated noise and delayed inhibitory feedback. Phys Rev E Stat Nonlin Soft Matter Phys 72, 061919.
68. Maimon, G. and J. A. Assad. 2009. Beyond Poisson: Increased spike-time regularity across primate parietal cortex. Neuron 62, 426-440.
69. Markram, H. 2006. The blue brain project. Nat Rev Neurosci7, 153-160.
70. Markram, H., J. Lubke, M. Frotscher, A. Roth, and B. Sakmann. 1997. Physiology and anatomy of synaptic connections between thick tufted pyramidal neurones in the developing rat neocortex. J Physiol (Lond) 500, 409-440.
71. Marr, D. 1969. A theory of cerebellar cortex. J Physiol 202, 437-470.
72. Marr, D. 1970. A theory for cerebral neocortex. Proc Roy Soc. Lond B 176, 161-.
73. Marr, D. 1971. Simple memory: A theory for archicortex. Philos Trans Roy Soc Lond B 262, 23-81.
74. Mazzoni, A., S. Panzeri, N. K. Logothetis, and N. Brunel. 2008. Encoding of naturalistic stimuli by local field potential spectra in networks of excitatory and inhibitory neurons. PLoS Comput Biol 4, e1000239.
75. McCulloch, W. S. and W. A. Pitts. 1943. A logical calculus of the ideas immanent in nervous activity. Bull Math Biophys 5, 115-133.
76. Meffin, H., A. N. Burkitt, and D. B. Grayden. 2004. An analytical model for the “large, fluctuating synaptic conductance state” typical of neocortical neurons in vivo. J Comput Neurosci 16, 159-175.
77. Monteforte, M. and F. Wolf. 2010. Dynamical entropy production in spiking neuron networks in the balanced state. Phys Rev Lett 105, 268104.
78. Naud, R., N. Marcille, C. Clopath, and W. Gerstner. 2008. Firing patterns in the adaptive exponential integrate-and-fire model. Biol Cybern 99, 335-347.
79. O’Connor, D. H., S. P. Peron, D. Huber, and K. Svoboda. 2010. Neural activity in barrel cortex underlying vibrissa-based object localization in mice. Neuron 67, 1048-1061.
80. Ostojic, S. and N. Brunel. 2011. From spiking neuron models to linear-nonlinear models. PLOS Comp Biol 7, e1001056.
81. Ostojic, S., N. Brunel, and V. Hakim. 2009. How connectivity, background activity, and synaptic properties shape the cross-correlation between spike trains. J Neurosci 29, 10234-10253.
82. Perez-Orive, J., O. Mazor, G. Turner, S. Cassenaer, R. Wilson, and G. Laurent. 2002. Oscillations and sparsening of odor representations in the mushroom body. Science 297, 359-365.
83. Politi, A., R. Livi, G. L. Oppo, and R. Kapral. 1993. Unpredictable behavior in stable systems. Europhys Lett22, 571-576.
84. Renart, A., J. de la Rocha, P. Bartho, L. Hollender, N. Parga, A. Reyes, and K. D. Harris. 2010. The asynchronous state in cortical circuits. Science 327, 587-590.
85. Richardson, M., N. Brunel, and V. Hakim. 2003. From subthreshold to firing-rate resonance. J Neurophysiol 89, 2538-2554.
86. Richardson, M. J. and R. Swarbrick. 2010. Firing-rate response of a neuron receiving excitatory and inhibitory synaptic shot noise. Phys Rev Lett 105, 178102.
87. Richardson, M. J. E. 2007. Firing-rate response of linear and nonlinear integrate-and-fire neurons to modulated current-based and conductance-based synaptic drive. Phys Rev E Stat Nonlin Soft Matter Phys 76, 021919.
88. Roxin, A. 2011. The role of degree distribution in shaping the dynamics in networks of sparsely connected spiking neurons. Front Comput Neurosci 5, 8.
89. Roxin, A., N. Brunel, and D. Hansel. 2005. Role of delays in shaping spatiotemporal dynamics of neuronal activity in large networks. Phys Rev Lett 94, 238103.
90. Roxin, A., N. Brunel, D. Hansel, G. Mongillo, and C. van Vreeswijk. 2011. On the distribution of firing rates in networks of cortical neurons. J Neurosci 9, 31(45), 16217-16226.
91. Shafi, M., Y. Zhou, J. Quintana, C. Chow, J. Fuster, and M. Bodner. 2007. Variability in neuronal activity in primate cortex during working memory tasks. Neuroscience 146, 1082-1108.
92. Shea-Brown, E., K. Josic, J. de la Rocha, and B. Doiron. 2008. Correlation and synchrony transfer in integrate-and-fire neurons: Basic properties and consequences for coding. Phys Rev Lett 100, 108102.
93. Smith, M. A. and A. Kohn. 2008. Spatial and temporal scales of neuronal correlation in primary visual cortex. J Neurosci 28, 12591-12603.
94. Softky, W. R. and C. Koch. 1993. The highly irregular firing of cortical cells is inconsistent with temporal integration of random EPSPs. J. Neurosci 13, 334-350.
95. Song, S., P. J. Sjostrom, M. Reigl, S. Nelson, and D. B. Chklovskii. 2005. Highly nonrandom features of synaptic connectivity in local cortical circuits. PLoS Biol 3, e68.
96. Stein, R. 1965. A theoretical analysis of neuronal variability. Biophys. J 5, 173-194.
97. Tabak, J., W. Senn, M. J. O’Donovan, and J. Rinzel. 2000. Modeling of spontaneous activity in developing spinal cord using activity-dependent depression in an excitatory network. J Neurosci 20, 3041-3056.
98. Tchumatchenko, T., A. Malyshev, T. Geisel, M. Volgushev, and F. Wolf. 2010. Correlations and synchrony in threshold neuron models. Phys Rev Lett 104, 058102.
99. Touboul, J. 2008. Bifurcation analysis of a general class of nonlinear integrate-and-fire neurons. SIAM J Appl Math 68, 1045-1079.
100. Touboul, J. and R. Brette. 2008. Dynamics and bifurcations of the adaptive exponential integrate-and-fire model. Biol Cybern 99, 319-334.
101. Treves, A. 1993. Mean-field analysis of neuronal spike dynamics. Network 4, 259-284.
102. Tsodyks, M., A. Uziel, and H. Markram. 2000. Synchrony generation in recurrent networks with frequency-dependent synapses. J Neurosci 20, RC50.
103. Tsodyks, M. V., W. E. Skaggs, T. J. Sejnowski, and B. L. McNaughton. 1997. Paradoxical effects of external modulation of inhibitory interneurons. J Neurosci 17, 4382-4388.
104. Tsodyks, M. V. and H. Markram. 1997. The neural code between neocortical pyramidal neurons depends on neurotransmitter release probability. Proc Natl Acad Sci USA 94, 719-723.
105. Tsodyks, M. V., K. Pawelzik, and H. Markram. 1998. Neural networks with dynamic synapses. Neural Comput 10, 821-835.
106. Tuckwell, H. C. 1988. Introduction to Theoretical Neurobiology. Cambridge: Cambridge University Press.
107. van Vreeswijk, C. and H. Sompolinsky. 1996. Chaos in neuronal networks with balanced excitatory and inhibitory activity. Science 274, 1724-1726.
108. van Vreeswijk, C. and H. Sompolinsky. 1998. Chaotic balanced state in a model of cortical circuits. Neural Comput 10, 1321-1371.
109. Vogels, T. P. and L. F. Abbott. 2005. Signal propagation and logic gating in networks of integrate-and-fire neurons. J Neurosci 25, 10786-10795.
110. Vogels, T. P., K. Rajan, and L. F. Abbott. 2005. Neural network dynamics. Annu Rev Neurosci 28, 357-376.
111. Wang, X.-J. 1999. Synaptic basis of cortical persistent activity: The importance of NMDA receptors to working memory. J Neurosci 19, 9587-9603.
112. Wang, X.-J. and G. Buzsáki. 1996. Gamma oscillation by synaptic inhibition in a hippocampal interneuronal network model. J Neurosci 16, 6402-6413.
113. Wilson, H. R. and J. D. Cowan. 1972. Excitatory and inhibitory interactions in localized populations of model neurons. Biophys J 12, 1-24.
114. Wilson, H. R. and J. D. Cowan. 1973. A mathematical theory of the functional dynamics of cortical and thalamic nervous tissue. Kybernetik 13, 55-80.
115. Xie, X., R. H. R. Hahnloser, and H. S. Seung. 2002. Double-ring network model of the head direction system. Phys Rev E 66, 041902.
116. Zhang, K. 1996. Representation of spatial orientation by the intrinsic dynamics of the head-direction cell ensembles: A theory. J Neurosci 16, 2112-2126.
117. Zillmer, R., N. Brunel, and D. Hansel. 2009. Very long transients, irregular firing, and chaotic dynamics in networks of randomly connected inhibitory integrate-and-fire neurons. Phys Rev E Stat Nonlin Soft Matter Phys 79, 031909.
118. Zillmer, R., R. Livi, A. Politi, and A. Torcini. 2006. Desynchronization in diluted neural networks. Phys Rev E Stat Nonlin Soft Matter Phys 74, 036203.