H P McKean. Proc Natl Acad Sci U S A 1966

**Times Cited: 15**Times Cited

Times Co-cited

Similarity

Mean-field description and propagation of chaos in networks of Hodgkin-Huxley and FitzHugh-Nagumo neurons.

Javier Baladron, Diego Fasoli, Olivier Faugeras, Jonathan Touboul. J Math Neurosci 2012

Javier Baladron, Diego Fasoli, Olivier Faugeras, Jonathan Touboul. J Math Neurosci 2012

33

Systematic fluctuation expansion for neural network activity equations.

Michael A Buice, Jack D Cowan, Carson C Chow. Neural Comput 2010

Michael A Buice, Jack D Cowan, Carson C Chow. Neural Comput 2010

26

A constructive mean-field analysis of multi-population neural networks with random synaptic weights and stochastic inputs.

Olivier Faugeras, Jonathan Touboul, Bruno Cessac. Front Comput Neurosci 2009

Olivier Faugeras, Jonathan Touboul, Bruno Cessac. Front Comput Neurosci 2009

26

Excitatory and inhibitory interactions in localized populations of model neurons.

H R Wilson, J D Cowan. Biophys J 1972

H R Wilson, J D Cowan. Biophys J 1972

26

Asynchronous states in networks of pulse-coupled oscillators.

Abbott, van Vreeswijk C. Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics 1993

Abbott, van Vreeswijk C. Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics 1993

26

Time structure of the activity in neural network models.

Gerstner. Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics 1995

Gerstner. Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics 1995

26

Dynamics of sparsely connected networks of excitatory and inhibitory spiking neurons.

N Brunel. J Comput Neurosci 2000

N Brunel. J Comput Neurosci 2000

20

Population dynamics of interacting spiking neurons.

Maurizio Mattia, Paolo Del Giudice. Phys Rev E Stat Nonlin Soft Matter Phys 2002

Maurizio Mattia, Paolo Del Giudice. Phys Rev E Stat Nonlin Soft Matter Phys 2002

20

An effective kinetic representation of fluctuation-driven neuronal networks with application to simple and complex cells in visual cortex.

David Cai, Louis Tao, Michael Shelley, David W McLaughlin. Proc Natl Acad Sci U S A 2004

David Cai, Louis Tao, Michael Shelley, David W McLaughlin. Proc Natl Acad Sci U S A 2004

20

20

Fast global oscillations in networks of integrate-and-fire neurons with low firing rates.

N Brunel, V Hakim. Neural Comput 1999

N Brunel, V Hakim. Neural Comput 1999

20

A mathematical theory of the functional dynamics of cortical and thalamic nervous tissue.

H R Wilson, J D Cowan. Kybernetik 1973

H R Wilson, J D Cowan. Kybernetik 1973

20

Field-theoretic approach to fluctuation effects in neural networks.

Michael A Buice, Jack D Cowan. Phys Rev E Stat Nonlin Soft Matter Phys 2007

Michael A Buice, Jack D Cowan. Phys Rev E Stat Nonlin Soft Matter Phys 2007

20

Kinetic theory of coupled oscillators.

Eric J Hildebrand, Michael A Buice, Carson C Chow. Phys Rev Lett 2007

Eric J Hildebrand, Michael A Buice, Carson C Chow. Phys Rev Lett 2007

20

Effective stochastic behavior in dynamical systems with incomplete information.

Michael A Buice, Carson C Chow. Phys Rev E Stat Nonlin Soft Matter Phys 2011

Michael A Buice, Carson C Chow. Phys Rev E Stat Nonlin Soft Matter Phys 2011

75

The number of synaptic inputs and the synchrony of large, sparse neuronal networks.

D Golomb, D Hansel. Neural Comput 2000

D Golomb, D Hansel. Neural Comput 2000

20

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

W Gerstner. Neural Comput 2000

W Gerstner. Neural Comput 2000

20

Correlations, fluctuations, and stability of a finite-size network of coupled oscillators.

Michael A Buice, Carson C Chow. Phys Rev E Stat Nonlin Soft Matter Phys 2007

Michael A Buice, Carson C Chow. Phys Rev E Stat Nonlin Soft Matter Phys 2007

20

The highly irregular firing of cortical cells is inconsistent with temporal integration of random EPSPs.

W R Softky, C Koch. J Neurosci 1993

W R Softky, C Koch. J Neurosci 1993

13

A quantitative description of membrane current and its application to conduction and excitation in nerve.

A L HODGKIN, A F HUXLEY. J Physiol 1952

A L HODGKIN, A F HUXLEY. J Physiol 1952

13

A master equation formalism for macroscopic modeling of asynchronous irregular activity states.

Sami El Boustani, Alain Destexhe. Neural Comput 2009

Sami El Boustani, Alain Destexhe. Neural Comput 2009

13

Critical analysis of dimension reduction by a moment closure method in a population density approach to neural network modeling.

Cheng Ly, Daniel Tranchina. Neural Comput 2007

Cheng Ly, Daniel Tranchina. Neural Comput 2007

13

Chaos in neuronal networks with balanced excitatory and inhibitory activity.

C van Vreeswijk, H Sompolinsky. Science 1996

C van Vreeswijk, H Sompolinsky. Science 1996

13

A population density approach that facilitates large-scale modeling of neural networks: extension to slow inhibitory synapses.

D Q Nykamp, D Tranchina. Neural Comput 2001

D Q Nykamp, D Tranchina. Neural Comput 2001

13

A population density approach that facilitates large-scale modeling of neural networks: analysis and an application to orientation tuning.

D Q Nykamp, D Tranchina. J Comput Neurosci 2000

D Q Nykamp, D Tranchina. J Comput Neurosci 2000

13

Dynamics of the firing probability of noisy integrate-and-fire neurons.

Nicolas Fourcaud, Nicolas Brunel. Neural Comput 2002

Nicolas Fourcaud, Nicolas Brunel. Neural Comput 2002

13

Chaotic balanced state in a model of cortical circuits.

C van Vreeswijk, H Sompolinsky. Neural Comput 1998

C van Vreeswijk, H Sompolinsky. Neural Comput 1998

13

Geometric visual hallucinations, Euclidean symmetry and the functional architecture of striate cortex.

P C Bressloff, J D Cowan, M Golubitsky, P J Thomas, M C Wiener. Philos Trans R Soc Lond B Biol Sci 2001

P C Bressloff, J D Cowan, M Golubitsky, P J Thomas, M C Wiener. Philos Trans R Soc Lond B Biol Sci 2001

13

13

13

Dynamic finite size effects in spiking neural networks.

Michael A Buice, Carson C Chow. PLoS Comput Biol 2013

Michael A Buice, Carson C Chow. PLoS Comput Biol 2013

13

Neurons with graded response have collective computational properties like those of two-state neurons.

J J Hopfield. Proc Natl Acad Sci U S A 1984

J J Hopfield. Proc Natl Acad Sci U S A 1984

13

Dynamical behavior of stochastic systems of infinitely many coupled nonlinear oscillators exhibiting phase transitions of mean-field type: H theorem on asymptotic approach to equilibrium and critical slowing down of order-parameter fluctuations.

Shiino. Phys Rev A Gen Phys 1987

Shiino. Phys Rev A Gen Phys 1987

13

Noise-induced transitions in rugged energy landscapes.

A B Duncan, S Kalliadasis, G A Pavliotis, M Pradas. Phys Rev E 2016

A B Duncan, S Kalliadasis, G A Pavliotis, M Pradas. Phys Rev E 2016

100

General dynamical density functional theory for classical fluids.

Benjamin D Goddard, Andreas Nold, Nikos Savva, Grigorios A Pavliotis, Serafim Kalliadasis. Phys Rev Lett 2012

Benjamin D Goddard, Andreas Nold, Nikos Savva, Grigorios A Pavliotis, Serafim Kalliadasis. Phys Rev Lett 2012

13

Variance Reduction Using Nonreversible Langevin Samplers.

A B Duncan, T Lelièvre, G A Pavliotis. J Stat Phys 2016

A B Duncan, T Lelièvre, G A Pavliotis. J Stat Phys 2016

22

Complete Mean-Field Theory for Dynamics of Binary Recurrent Networks.

Farzad Farkhooi, Wilhelm Stannat. Phys Rev Lett 2017

Farzad Farkhooi, Wilhelm Stannat. Phys Rev Lett 2017

40

Mean Field Limits for Interacting Diffusions in a Two-Scale Potential.

S N Gomes, G A Pavliotis. J Nonlinear Sci 2018

S N Gomes, G A Pavliotis. J Nonlinear Sci 2018

66

Model of global spontaneous activity and local structured activity during delay periods in the cerebral cortex.

D J Amit, N Brunel. Cereb Cortex 1997

D J Amit, N Brunel. Cereb Cortex 1997

6

Dynamics of coherently pumped lasers with linearly polarized pump and generated fields.

Corbalán, Vilaseca, Arjona, Pujol, Roldán, de Valcárcel GJ. Phys Rev A 1993

Corbalán, Vilaseca, Arjona, Pujol, Roldán, de Valcárcel GJ. Phys Rev A 1993

7

Phase transitions towards criticality in a neural system with adaptive interactions.

Anna Levina, J Michael Herrmann, Theo Geisel. Phys Rev Lett 2009

Anna Levina, J Michael Herrmann, Theo Geisel. Phys Rev Lett 2009

6

Firing rate of the noisy quadratic integrate-and-fire neuron.

Nicolas Brunel, Peter E Latham. Neural Comput 2003

Nicolas Brunel, Peter E Latham. Neural Comput 2003

6

Master-equation approach to stochastic neurodynamics.

Ohira, Cowan. Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics 1993

Ohira, Cowan. Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics 1993

6

Theoretical effect of temperature on threshold in the Hodgkin-Huxley nerve model.

R Fitzhugh. J Gen Physiol 1966

R Fitzhugh. J Gen Physiol 1966

6

Synthesis of models for excitable membranes, synaptic transmission and neuromodulation using a common kinetic formalism.

A Destexhe, Z F Mainen, T J Sejnowski. J Comput Neurosci 1994

A Destexhe, Z F Mainen, T J Sejnowski. J Comput Neurosci 1994

6

Hyperbolic planforms in relation to visual edges and textures perception.

Pascal Chossat, Olivier Faugeras. PLoS Comput Biol 2009

Pascal Chossat, Olivier Faugeras. PLoS Comput Biol 2009

7

Population model of hippocampal pyramidal neurons, linking a refractory density approach to conductance-based neurons.

Anton V Chizhov, Lyle J Graham. Phys Rev E Stat Nonlin Soft Matter Phys 2007

Anton V Chizhov, Lyle J Graham. Phys Rev E Stat Nonlin Soft Matter Phys 2007

6

Co-cited is the co-citation frequency, indicating how many articles cite the article together with the query article. Similarity is the co-citation as percentage of the times cited of the query article or the article in the search results, whichever is the lowest. These numbers are calculated for the last 100 citations when articles are cited more than 100 times.