Citation Relationships



Nykamp DQ, Tranchina D (2000) A population density approach that facilitates large-scale modeling of neural networks: analysis and an application to orientation tuning. J Comput Neurosci 8:19-50 [PubMed]

References and models cited by this paper

References and models that cite this paper

Abbott LF, van Vreeswijk C (1993) Asynchronous states in networks of pulse-coupled oscillators. Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics 48:1483-1490 [PubMed]

Adorjan P, Barna G, Erdi P, Obermayer K (1999) A statistical neural field approach to orientation selectivity Neurocomputing 27:477-482

Amari S (1974) A method of statistical neurodynamics. Kybernetik 14:201-15 [PubMed]

Barna G, Gróbler T, Erdi P (1998) Statistical model of the hippocampal CA3 region II. The population framework: model of rhythmic activity in the CA3 slice. Biol Cybern 79:309-21 [Journal] [PubMed]

Ben-Yishai R, Bar-Or RL, Sompolinsky H (1995) Theory of orientation tuning in visual cortex. Proc Natl Acad Sci U S A 92:3844-8 [PubMed]

Brunel N, Hakim V (1999) Fast global oscillations in networks of integrate-and-fire neurons with low firing rates. Neural Comput 11:1621-71 [PubMed]

   Fast global oscillations in networks of I&F neurons with low firing rates (Brunel and Hakim 1999) [Model]

Carandini M, Ringach DL (1997) Predictions of a recurrent model of orientation selectivity. Vision Res 37:3061-71 [PubMed]

Chawanya T, Aoyagi T, Nishikawa I, Okuda K, Kuramoto Y (1993) A model for feature linking via collective oscillations in the primary visual cortex. Biol Cybern 68:483-90 [PubMed]

Cinlar E (1972) Superposition of point processes Stochastic point processes, Lewis PAW, ed. pp.549

Crank J, Nicolson P (1947) A practical method for numerical evaluation of solutions for partial differential equations of the heat conduction type Proc Camb Philos Sco 43:50-67

Gerstner W (1995) Time structure of the activity in neural network models. Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics 51:738-758 [PubMed]

Gerstner W (2000) Population dynamics of spiking neurons: fast transients, asynchronous states, and locking. Neural Comput 12:43-89 [PubMed]

Gerstner W, van Hemmen JL (1994) Coding and information processing in neural networks. Models Of Neural Networks, Domany E:van Hemmen JL:Schulten K, ed. pp.1

Hansel D, Sompolinsky H (1996) Chaos and synchrony in a model of a hypercolumn in visual cortex. J Comput Neurosci 3:7-34 [PubMed]

Howe JR, Sutor B, Zieglgänsberger W (1987) Baclofen reduces post-synaptic potentials of rat cortical neurones by an action other than its hyperpolarizing action. J Physiol 384:539-69 [PubMed]

Knight BW (1972) Dynamics of encoding in a population of neurons. J Gen Physiol 59:734-66 [PubMed]

Knight BW (1972) The relationship between the firing rate of a single neuron and the level of activity in a population of neurons. Experimental evidence for resonant enhancement in the population response. J Gen Physiol 59:767-78 [PubMed]

Knight BW (2000) Dynamics of encoding in neuron populations: some general mathematical features. Neural Comput 12:473-518 [PubMed]

Knight BW, Manin D, Sirovich L (1996) Dynamical models of interacting neuron populations Symposium on Robotics and Cybernetics: Computational Engineering in Systems Applications, Gerf EC, ed.

Kuramoto Y (1991) Collective synchronization of pulse-coupled oscillators and excitable units Physica D 50:15-30

Omurtag A, Knight BW, Sirovich L (2000) On the simulation of large populations of neurons. J Comput Neurosci 8:51-63 [PubMed]

Sirovich L, Knight BW, Omurtag A (2000) Dynamics of neuronal populations: The equilibrium solution. Siam J Applied Math 60:2009-2028

Somers DC, Nelson SB, Sur M (1995) An emergent model of orientation selectivity in cat visual cortical simple cells. J Neurosci 15:5448-65 [PubMed]

Sompolinsky H, Shapley R (1997) New perspectives on the mechanisms for orientation selectivity. Curr Opin Neurobiol 7:514-22 [PubMed]

Strogatz SH, Mirollo RE (1991) Stability of incoherence in a population of coupled oscillators J Stat Phys 63:613-635

Tanabe S, Pakdaman K, Nomura T, Sato S (1998) Dynamics of an ensemble of leaky integrate-and-fire neuron models and its response to a pulse input Technical Report of IEICE 14:41-48

Treves A (1993) Mean field analysis of neuronal spike dynamics. Network 4:259-284

Tuckwell HC (1988) Introduction to Theoretical Neurobiology. Volume 2: Nonlinear and Stochastic Theories

Vibert JF, Champagnat J, Pakdaman K, Pham J (1998) Activity in sparsely connected excitatory neural networks: effect of connectivity. Neural Netw 11:415-434 [PubMed]

Victor JD (1987) The dynamics of the cat retinal X cell centre. J Physiol 386:219-46 [PubMed]

Wilbur WJ, Rinzel J (1983) A theoretical basis for large coefficient of variation and bimodality in neuronal interspike interval distributions. J Theor Biol 105:345-68 [PubMed]

Wilson HR, Cowan JD (1972) Excitatory and inhibitory interactions in localized populations of model neurons. Biophys J 12:1-24 [Journal] [PubMed]

   Excitatory and inhibitory interactions in populations of model neurons (Wilson and Cowan 1972) [Model]

Wilson HR, Cowan JD (1973) A mathematical theory of the functional dynamics of cortical and thalamic nervous tissue. Kybernetik 13:55-80 [PubMed]

Brown E, Moehlis J, Holmes P (2004) On the phase reduction and response dynamics of neural oscillator populations. Neural Comput 16:673-715 [Journal] [PubMed]

Brown E, Moehlis J, Holmes P, Clayton E, Rajkowski J, Aston-Jones G (2004) The influence of spike rate and stimulus duration on noradrenergic neurons. J Comput Neurosci 17:13-29 [Journal] [PubMed]

Câteau H, Reyes AD (2006) Relation between single neuron and population spiking statistics and effects on network activity. Phys Rev Lett 96:058101 [Journal] [PubMed]

Droste F, Lindner B (2017) Exact analytical results for integrate-and-fire neurons driven by excitatory shot noise J. Comp. Neurosci. [Journal]

   Theory and simulation of integrate-and-fire neurons driven by shot noise (Droste & Lindner 2017) [Model]

Eggert J, van Hemmen JL (2001) Modeling neuronal assemblies: theory and implementation. Neural Comput 13:1923-74 [Journal] [PubMed]

Huertas MA, Groff JR, Smith GD (2005) Feedback inhibition and throughput properties of an integrate-and-fire-or-burst network model of retinogeniculate transmission. J Comput Neurosci 19:147-80 [Journal] [PubMed]

Huertas MA, Smith GD (2006) A multivariate population density model of the dLGN/PGN relay. J Comput Neurosci 21:171-89 [Journal] [PubMed]

La Camera G, Rauch A, Lüscher HR, Senn W, Fusi S (2004) Minimal models of adapted neuronal response to in vivo-like input currents. Neural Comput 16:2101-24 [Journal] [PubMed]

Linaro D, Storace M, Giugliano M (2011) Accurate and fast simulation of channel noise in conductance-based model neurons by diffusion approximation. PLoS Comput Biol 7:e1001102 [Journal] [PubMed]

   Accurate and fast simulation of channel noise in conductance-based model neurons (Linaro et al 2011) [Model]

Ly C, Tranchina D (2007) Critical analysis of dimension reduction by a moment closure method in a population density approach to neural network modeling. Neural Comput 19:2032-92 [Journal] [PubMed]

Muller E, Buesing L, Schemmel J, Meier K (2007) Spike-frequency adapting neural ensembles: beyond mean adaptation and renewal theories. Neural Comput 19:2958-3010 [Journal] [PubMed]

Nicola W, Campbell SA (2013) Bifurcations of large networks of two-dimensional integrate and fire neurons. J Comput Neurosci 35:87-108 [Journal] [PubMed]

   Mean Field Equations for Two-Dimensional Integrate and Fire Models (Nicola and Campbell, 2013) [Model]

Omurtag A, Knight BW, Sirovich L (2000) On the simulation of large populations of neurons. J Comput Neurosci 8:51-63 [PubMed]

Shelley M, McLaughlin D (2002) Coarse-grained reduction and analysis of a network model of cortical response: I. Drifting grating stimuli. J Comput Neurosci 12:97-122 [PubMed]

Soula H, Chow CC (2007) Stochastic dynamics of a finite-size spiking neural network. Neural Comput 19:3262-92 [Journal] [PubMed]

Troyer TW (2006) Factors affecting phase synchronization in integrate-and-fire oscillators. J Comput Neurosci 20:191-200 [Journal] [PubMed]

Van Rossum MC (2001) The transient precision of integrate and fire neurons: effect of background activity and noise. J Comput Neurosci 10:303-11 [Journal] [PubMed]

Visser S, Van Gils SA (2014) Lumping Izhikevich neurons EPJ Nonlinear Biomedical Physics 25(12):6 [Journal]

   Norns - Neural Network Studio (Visser & Van Gils 2014) [Model]

(51 refs)