HOME HELP FEEDBACK SUBSCRIPTIONS ARCHIVE SEARCH TABLE OF CONTENTS		QUICK SEARCH:   [advanced] Author: Keyword(s): Year:  Vol:  Page:

This Article Full Text Full Text (PDF) Alert me when this article is cited Alert me if a correction is posted Services Similar articles in this journal Similar articles in PubMed Alert me to new issues of the journal Download to citation manager Citing Articles Citing Articles via HighWire Citing Articles via Google Scholar Google Scholar Articles by Gerstner, W. Search for Related Content PubMed PubMed Citation Articles by Gerstner, W.

Population Dynamics of Spiking Neurons: Fast Transients, Asynchronous States, and Locking

Center for Neuromimetic Systems, Swiss Federal Institute of Technology, EPFL-DI, CH-1015 Lausanne, Switzerland

An integral equation describing the time evolution of the population activity in a homogeneous pool of spiking neurons of the integrate-and-fire type is discussed. It is analytically shown that transients from a state of incoherent firing can be immediate. The stability of incoherent firing is analyzed in terms of the noise level and transmission delay, and a bifurcation diagram is derived. The response of a population of noisy integrate-and-fire neurons to an input current of small amplitude is calculated and characterized by a linear filter . The stability of perfectly synchronized "locked" solutions is analyzed.

This article has been cited by other articles:

				H. Kondgen, C. Geisler, S. Fusi, X.-J. Wang, H.-R. Luscher, and M. Giugliano The Dynamical Response Properties of Neocortical Neurons to Temporally Modulated Noisy Inputs In Vitro Cereb Cortex, September 1, 2008; 18(9): 2086 - 2097. [Abstract] [Full Text] [PDF]

				M. C. W. van Rossum, M. A. A. van der Meer, D. Xiao, and M. W. Oram Adaptive Integration in the Visual Cortex by Depressing Recurrent Cortical Circuits Neural Comput., July 1, 2008; 20(7): 1847 - 1872. [Abstract] [Full Text] [PDF]

				A. Kumar, S. Rotter, and A. Aertsen Conditions for Propagating Synchronous Spiking and Asynchronous Firing Rates in a Cortical Network Model J. Neurosci., May 14, 2008; 28(20): 5268 - 5280. [Abstract] [Full Text] [PDF]

				Z. Pawlas, L. B. Klebanov, M. Prokop, and P. Lansky Parameters of Spike Trains Observed in a Short Time Window Neural Comput., May 1, 2008; 20(5): 1325 - 1343. [Abstract] [Full Text] [PDF]

				T. M. Hospedales, M. C. W. van Rossum, B. P. Graham, and M. B. Dutia Implications of noise and neural heterogeneity for vestibulo-ocular reflex fidelity. Neural Comput., March 1, 2008; 20(3): 756 - 778. [Abstract] [Full Text] [PDF]

				L. Badel, S. Lefort, R. Brette, C. C. H. Petersen, W. Gerstner, and M. J. E. Richardson Dynamic I-V Curves Are Reliable Predictors of Naturalistic Pyramidal-Neuron Voltage Traces J Neurophysiol, February 1, 2008; 99(2): 656 - 666. [Abstract] [Full Text] [PDF]

				H. Soula and C. C. Chow Stochastic dynamics of a finite-size spiking neural network. Neural Comput., December 1, 2007; 19(12): 3262 - 3292. [Abstract] [Full Text] [PDF]

				E. Muller, L. Buesing, J. Schemmel, and K. Meier Spike-Frequency Adapting Neural Ensembles: Beyond Mean Adaptation and Renewal Theories Neural Comput., November 1, 2007; 19(11): 2958 - 3010. [Abstract] [Full Text] [PDF]

				A. Kaltenbrunner, V. Gomez, and V. Lopez Phase Transition and Hysteresis in an Ensemble of Stochastic Spiking Neurons Neural Comput., November 1, 2007; 19(11): 3011 - 3050. [Abstract] [Full Text] [PDF]

				N. Masuda, M. Okada, and K. Aihara Filtering of spatial bias and noise inputs by spatially structured neural networks. Neural Comput., July 1, 2007; 19(7): 1854 - 1870. [Abstract] [Full Text] [PDF]

				S. Wu, K. Hamaguchi, and S.-i. Amari Dynamics and Computation of Continuous Attractors Neural Comput., April 1, 2007; 20(4): 994 - 1025. [Abstract] [Full Text] [PDF]

				C. Geisler, N. Brunel, and X.-J. Wang Contributions of Intrinsic Membrane Dynamics to Fast Network Oscillations With Irregular Neuronal Discharges J Neurophysiol, December 1, 2005; 94(6): 4344 - 4361. [Abstract] [Full Text] [PDF]

				N. Masuda, B. Doiron, A. Longtin, and K. Aihara Coding of Temporally Varying Signals in Networks of Spiking Neurons with Global Delayed Feedback Neural Comput., October 1, 2005; 17(10): 2139 - 2175. [Abstract] [Full Text] [PDF]

				C. Borgers and N. Kopell Effects of Noisy Drive on Rhythms in Networks of Excitatory and Inhibitory Neurons Neural Comput., March 1, 2005; 17(3): 557 - 608. [Abstract] [Full Text] [PDF]

				H. Soula, G. Beslon, and O. Mazet Spontaneous Dynamics of Asymmetric Random Recurrent Spiking Neural Networks Neural Comput., January 1, 2005; 18(1): 60 - 79. [Abstract] [Full Text] [PDF]

				G. La Camera, A. Rauch, H.-R. Luscher, W. Senn, and S. Fusi Minimal Models of Adapted Neuronal Response to In Vivo-Like Input Currents Neural Comput., October 1, 2004; 16(10): 2101 - 2124. [Abstract] [Full Text] [PDF]

				D. Cai, L. Tao, and D. W. McLaughlin An embedded network approach for scale-up of fluctuation-driven systems with preservation of spike information PNAS, September 28, 2004; 101(39): 14288 - 14293. [Abstract] [Full Text] [PDF]

				M. Giugliano, P. Darbon, M. Arsiero, H.-R. Luscher, and J. Streit Single-Neuron Discharge Properties and Network Activity in Dissociated Cultures of Neocortex J Neurophysiol, August 1, 2004; 92(2): 977 - 996. [Abstract] [Full Text] [PDF]

				D. Cai, L. Tao, M. Shelley, and D. W. McLaughlin An effective kinetic representation of fluctuation-driven neuronal networks with application to simple and complex cells in visual cortex PNAS, May 18, 2004; 101(20): 7757 - 7762. [Abstract] [Full Text] [PDF]

				E. Brown, J. Moehlis, and P. Holmes On the Phase Reduction and Response Dynamics of Neural Oscillator Populations Neural Comput., April 1, 2004; 16(4): 673 - 715. [Abstract] [Full Text] [PDF]

				N. Masuda and K. Aihara Self-Organizing Dual Coding Based on Spike-Time-Dependent Plasticity Neural Comput., March 1, 2004; 16(3): 627 - 663. [Abstract] [Full Text] [PDF]

				P.H.E. Tiesinga and T.J. Sejnowski Rapid Temporal Modulation of Synchrony by Competition in Cortical Interneuron Networks Neural Comput., February 1, 2004; 16(2): 251 - 275. [Abstract] [Full Text] [PDF]

				N. Fourcaud-Trocme, D. Hansel, C. van Vreeswijk, and N. Brunel How Spike Generation Mechanisms Determine the Neuronal Response to Fluctuating Inputs J. Neurosci., December 17, 2003; 23(37): 11628 - 11640. [Abstract] [Full Text] [PDF]

				R. Maex and E. De Schutter Resonant Synchronization in Heterogeneous Networks of Inhibitory Neurons J. Neurosci., November 19, 2003; 23(33): 10503 - 10514. [Abstract] [Full Text] [PDF]

				O. Shriki, D. Hansel, and H. Sompolinsky Rate Models for Conductance-Based Cortical Neuronal Networks Neural Comput., August 1, 2003; 15(8): 1809 - 1841. [Abstract] [Full Text]

				M. J. E. Richardson, N. Brunel, and V. Hakim From Subthreshold to Firing-Rate Resonance J Neurophysiol, May 1, 2003; 89(5): 2538 - 2554. [Abstract] [Full Text] [PDF]

				D. Hansel and G. Mato Asynchronous States and the Emergence of Synchrony in Large Networks of Interacting Excitatory and Inhibitory Neurons Neural Comput., January 1, 2003; 15(1): 1 - 56. [Abstract] [Full Text] [PDF]

				N. Fourcaud and N. Brunel Dynamics of the Firing Probability of Noisy Integrate-and-Fire Neurons Neural Comput., September 1, 2002; 14(9): 2057 - 2110. [Abstract] [Full Text] [PDF]

				G. Fuhrmann, H. Markram, and M. Tsodyks Spike Frequency Adaptation and Neocortical Rhythms J Neurophysiol, August 1, 2002; 88(2): 761 - 770. [Abstract] [Full Text] [PDF]

				T. Wennekers Dynamic Approximation of Spatiotemporal Receptive Fields in Nonlinear Neural Field Models Neural Comput., August 1, 2002; 14(8): 1801 - 1825. [Abstract] [Full Text] [PDF]

				D. Hansel and C. van Vreeswijk How Noise Contributes to Contrast Invariance of Orientation Tuning in Cat Visual Cortex J. Neurosci., June 15, 2002; 22(12): 5118 - 5128. [Abstract] [Full Text] [PDF]

				M. C. W. van Rossum, G. G. Turrigiano, and S. B. Nelson Fast Propagation of Firing Rates through Layered Networks of Noisy Neurons J. Neurosci., March 1, 2002; 22(5): 1956 - 1966. [Abstract] [Full Text] [PDF]

				C. Meyer and C. van Vreeswijk Temporal Correlations in Stochastic Networks of Spiking Neurons Neural Comput., February 1, 2002; 14(2): 369 - 404. [Abstract] [Full Text] [PDF]

				R. Kempter, W. Gerstner, and J. L. van Hemmen Intrinsic Stabilization of Output Rates by Spike-Based Hebbian Learning Neural Comput., December 1, 2001; 13(12): 2709 - 2741. [Abstract] [Full Text]

				K.-i. Amemori and S. Ishii Gaussian Process Approach to Spiking Neurons for Inhomogeneous Poisson Inputs Neural Comput., December 1, 2001; 13(12): 2763 - 2797. [Abstract] [Full Text]

				F. B. Rodriguez, A. Suarez, and V. Lopez Period Focusing Induced by Network Feedback in Populations of Noisy Integrate-and-Fire Neurons Neural Comput., November 1, 2001; 13(11): 2495 - 2516. [Abstract] [Full Text]

				C. R. Laing and C. C. Chow Stationary Bumps in Networks of Spiking Neurons Neural Comput., July 1, 2001; 13(7): 1473 - 1494. [Abstract] [Full Text]

				L. Neltner and D. Hansel On Synchrony of Weakly Coupled Neurons at Low Firing Rate Neural Comput., April 1, 2001; 13(4): 765 - 774. [Abstract] [Full Text]

				D. Q. Nykamp and D. Tranchina A Population Density Approach That Facilitates Large-Scale Modeling of Neural Networks: Extension to Slow Inhibitory Synapses Neural Comput., March 1, 2001; 13(3): 511 - 546. [Abstract] [Full Text]

				D. Golomb and D. Hansel The Number of Synaptic Inputs and the Synchrony of Large, Sparse Neuronal Networks Neural Comput., May 1, 2000; 12(5): 1095 - 1139. [Abstract] [Full Text]