Legends:  Link to a Model  Reference cited by multiple papers 
•  Fast global oscillations in networks of I&F neurons with low firing rates (Brunel and Hakim 1999) 
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 pulsecoupled oscillators. Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics 48:14831490 [PubMed] Abeles M (1991) Corticonics: Neural Circuits of the Cerebral Cortex. Abramowitz M, Stegun IA (1970) Handbook Of Mathematical Functions Amit D, Brunel N (1997) Dynamics of a recurrent network of spiking neurons before and following learning Network 8:373404 Amit DJ, Brunel N (1997) Model of global spontaneous activity and local structured activity during delay periods in the cerebral cortex. Cereb Cortex 7:23752 [PubMed] Bender CM, Orszag SA (1987) Advanced Mathematical Methods for Scientists and Engineers Bragin A, Jandó G, Nádasdy Z, Hetke J, Wise K, Buzsáki G (1995) Gamma (40100 Hz) oscillation in the hippocampus of the behaving rat. J Neurosci 15:4760 [PubMed] Braitenberg V, Schuz A (1991) Anatomy of the Cortex: Statistics and Geometry Buzsáki G, Chrobak JJ (1995) Temporal structure in spatially organized neuronal ensembles: a role for interneuronal networks. Curr Opin Neurobiol 5:50410 [PubMed] Buzsáki G, Horváth Z, Urioste R, Hetke J, Wise K (1992) Highfrequency network oscillation in the hippocampus. Science 256:10257 [PubMed] Chandrasekhar S (1943) Stochastic problems in physics and astronomy Rev Mod Phys 15:1 Csicsvari J, Hirase H, Czurko A, Buzsáki G (1998) Reliability and state dependence of pyramidal cellinterneuron synapses in the hippocampus: an ensemble approach in the behaving rat. Neuron 21:17989 [PubMed] Delaney KR, Gelperin A, Fee MS, Flores JA, Gervais R, Tank DW, Kleinfeld D (1994) Waves and stimulusmodulated dynamics in an oscillating olfactory network. Proc Natl Acad Sci U S A 91:66973 [PubMed] Eckhorn R, Frien A, Bauer R, Woelbern T, Kehr H (1993) High frequency (6090 Hz) oscillations in primary visual cortex of awake monkey. Neuroreport 4:2436 [PubMed] Fisahn A, Pike FG, Buhl EH, Paulsen O (1998) Cholinergic induction of network oscillations at 40 Hz in the hippocampus in vitro. Nature 394:1869 [Journal] [PubMed] Gardiner CW (1983) Handbook of Stochastic Methods for Physics, Chemistry and the Natural Sciences Gerstner W (1995) Time structure of the activity in neural network models. Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics 51:738758 [PubMed] Gerstner W, van Hemmen JL, Cowan JD (1996) What matters in neuronal locking? Neural Comput 8:165376 [PubMed] Golomb D, Rinzel J (1994) Clustering in globally coupled inhibitory neurons Physica D 72:259282 Gray CM (1994) Synchronous oscillations in neuronal systems: mechanisms and functions. J Comput Neurosci 1:1138 [PubMed] Gray CM, König P, Engel AK, Singer W (1989) Oscillatory responses in cat visual cortex exhibit intercolumnar synchronization which reflects global stimulus properties. Nature 338:3347 [Journal] [PubMed] Gray CM, McCormick DA (1996) Chattering cells: superficial pyramidal neurons contributing to the generation of synchronous oscillations in the visual cortex. Science 274:10913 [PubMed] Hansel D, Mato G, Meunier C (1995) Synchrony in excitatory neural networks. Neural Comput 7:30737 [PubMed] Hirsch MW, Smale S (1974) Differential Equations, Dynamical Systems and Linear Algebra Kopell N, LeMasson G (1994) Rhythmogenesis, amplitude modulation, and multiplexing in a cortical architecture. Proc Natl Acad Sci U S A 91:1058690 [PubMed] Kreiter AK, Singer W (1996) Stimulusdependent synchronization of neuronal responses in the visual cortex of the awake macaque monkey. J Neurosci 16:238196 [PubMed] Laurent G, Davidowitz H (1994) Encoding of olfactory information with oscillating neural assemblies. Science 265:18725 [Journal] [PubMed] MacLeod K, Laurent G (1996) Distinct mechanisms for synchronization and temporal patterning of odorencoding neural assemblies. Science 274:9769 [PubMed] Mirollo RE, Strogatz SH (1990) Synchronization of pulsecoupled biological oscillators. Siam J Appl Math 6:16451657 Prechtl JC, Cohen LB, Pesaran B, Mitra PP, Kleinfeld D (1997) Visual stimuli induce waves of electrical activity in turtle cortex. Proc Natl Acad Sci U S A 94:76216 [PubMed] Rappel WJ, Karma A (1996) NoiseInduced Coherence in Neural Networks. Phys Rev Lett 77:32563259 [Journal] [PubMed] Ritz R, Sejnowski TJ (1997) Synchronous oscillatory activity in sensory systems: new vistas on mechanisms. Curr Opin Neurobiol 7:53646 [PubMed] Sakaguchi H, Shinomoto S, Kuramoto Y (1988) Phase transitions and their bifurcation analysis in a large population of active rotators with meanfield coupling Prog Theor Phys 79:600607 Singer W, Gray CM (1995) Visual feature integration and the temporal correlation hypothesis. Annu Rev Neurosci 18:55586 [Journal] [PubMed] Stopfer M, Bhagavan S, Smith BH, Laurent G (1997) Impaired odour discrimination on desynchronization of odourencoding neural assemblies. Nature 390:704 [Journal] [PubMed] Strogatz SH, Mirollo RE (1991) Stability of incoherence in a population of coupled oscillators J Stat Phys 63:613635 Traub RD, Miles R, Wong RK (1989) Model of the origin of rhythmic population oscillations in the hippocampal slice. Science 243:131925 [PubMed] Traub RD, Whittington MA, Colling SB, Buzsáki G, Jefferys JG (1996) Analysis of gamma rhythms in the rat hippocampus in vitro and in vivo. J Physiol 493 ( Pt 2):47184 [PubMed] Treves A (1993) Mean field analysis of neuronal spike dynamics. Network 4:259284 Tsodyks MV, Sejnowski TJ (1995) Rapid state switching in balanced cortical network models Network 6:111124 Van Vreeswijk C, Abbott LF, Ermentrout GB (1994) When inhibition not excitation synchronizes neural firing. J Comput Neurosci 1:31321 [PubMed] van Vreeswijk C, Sompolinsky H (1996) Chaos in neuronal networks with balanced excitatory and inhibitory activity. Science 274:17246 [PubMed] Vreeswijk Cv (1996) Partial synchronization in populations of pulsecoupled oscillators. Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics 54:55225537 [PubMed] Wang XJ, Buzsáki G (1996) Gamma oscillation by synaptic inhibition in a hippocampal interneuronal network model. J Neurosci 16:640213 [Journal] [PubMed]
Wang XJ, Golomb D, Rinzel J (1995) Emergent spindle oscillations and intermittent burst firing in a thalamic model: specific neuronal mechanisms. Proc Natl Acad Sci U S A 92:557781 [PubMed] Whittington MA, Traub RD, Jefferys JG (1995) Synchronized oscillations in interneuron networks driven by metabotropic glutamate receptor activation. Nature 373:6125 [Journal] [PubMed] Ylinen A, Bragin A, Nádasdy Z, Jandó G, Szabó I, Sik A, Buzsáki G (1995) Sharp waveassociated highfrequency oscillation (200 Hz) in the intact hippocampus: network and intracellular mechanisms. J Neurosci 15:3046 [PubMed]  Alvarez FP, Destexhe A (2004) Simulating cortical network activity states constrained by intracellular recordings. Neurocomputing 58:285290 AnguloGarcia D, Berke JD, Torcini A (2016) Cell Assembly Dynamics of SparselyConnected Inhibitory Networks: A Simple Model for the Collective Activity of Striatal Projection Neurons. PLoS Comput Biol 12:e1004778 [Journal] [PubMed] Badel L, Lefort S, Brette R, Petersen CC, Gerstner W, Richardson MJ (2008) Dynamic IV curves are reliable predictors of naturalistic pyramidalneuron voltage traces. J Neurophysiol 99:65666 [Journal] [PubMed] Banerjee A (2006) On the sensitive dependence on initial conditions of the dynamics of networks of spiking neurons. J Comput Neurosci 20:32148 [Journal] [PubMed] Bathellier B, Lagier S, Faure P, Lledo PM (2006) Circuit properties generating gamma oscillations in a network model of the olfactory bulb. J Neurophysiol 95:267891 [Journal] [PubMed]
Börgers C, Kopell N (2005) Effects of noisy drive on rhythms in networks of excitatory and inhibitory neurons. Neural Comput 17:557608 [Journal] [PubMed] Brunel N (2000) Dynamics of sparsely connected networks of excitatory and inhibitory spiking neurons. J Comput Neurosci 8:183208 [PubMed]
Brunel N, Hansel D (2006) How noise affects the synchronization properties of recurrent networks of inhibitory neurons. Neural Comput 18:1066110 [Journal] [PubMed] Brunel N, Wang XJ (2001) Effects of neuromodulation in a cortical network model of object working memory dominated by recurrent inhibition. J Comput Neurosci 11:6385 [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] Cortes JM, Torres JJ, Marro J, Garrido PL, Kappen HJ (2006) Effects of fast presynaptic noise in attractor neural networks. Neural Comput 18:61433 [Journal] [PubMed] Destexhe A, Rudolph M, Paré D (2003) The highconductance state of neocortical neurons in vivo. Nat Rev Neurosci 4:73951 [Journal] [PubMed] Geisler C, Brunel N, Wang XJ (2005) Contributions of intrinsic membrane dynamics to fast network oscillations with irregular neuronal discharges. J Neurophysiol 94:434461 [Journal] [PubMed] Hamaguchi K, Okada M, Aihara K (2007) Variable timescales of repeated spike patterns in synfire chain with Mexicanhat connectivity. Neural Comput 19:246891 [Journal] [PubMed] Hansel D, Mato G (2003) Asynchronous states and the emergence of synchrony in large networks of interacting excitatory and inhibitory neurons. Neural Comput 15:156 [Journal] [PubMed] Harris KD, Dashevskiy T, Mendoza J, Garcia AJ, Ramirez JM, SheaBrown E (2017) Different roles for inhibition in the rhythmgenerating respiratory network. J Neurophysiol 118:20702088 [Journal] [PubMed]
Herrmann A, Gerstner W (2001) Noise and the PSTH response to current transients: I. General theory and application to the integrateandfire neuron. J Comput Neurosci 11:13551 [PubMed] Jercog D, Roxin A, Barthó P, Luczak A, Compte A, de la Rocha J (2017) UPDOWN cortical dynamics reflect state transitions in a bistable network. Elife [Journal] [PubMed]
Kaltenbrunner A, Gómez V, López V (2007) Phase transition and hysteresis in an ensemble of stochastic spiking neurons. Neural Comput 19:301150 [Journal] [PubMed] La Camera G, Rauch A, Lüscher HR, Senn W, Fusi S (2004) Minimal models of adapted neuronal response to in vivolike input currents. Neural Comput 16:210124 [Journal] [PubMed] Laing CR (2006) On the application of "equationfree modelling" to neural systems. J Comput Neurosci 20:523 [Journal] [PubMed] 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 19:203292 [Journal] [PubMed] Magalhães B, Hines M, Sterling T, Schüermann F (2019) Exploiting Flow Graph of System of ODEs to Accelerate the Simulation of BiologicallyDetailed Neural Networks 2019 IEEE International Parallel and Distributed Processing Symposium (IPDPS) :176187 [Journal]
MäkiMarttunen T, Acimovic J, Ruohonen K, Linne ML (2013) Structuredynamics relationships in bursting neuronal networks revealed using a prediction framework. PLoS One 8:e69373 [Journal] [PubMed]
Marpeau F, Barua A, Josic K (2009) A finite volume method for stochastic integrateandfire models. J Comput Neurosci 26:44557 [Journal] [PubMed]
Masuda N, Doiron B, Longtin A, Aihara K (2005) Coding of temporally varying signals in networks of spiking neurons with global delayed feedback. Neural Comput 17:213975 [Journal] [PubMed] Meffin H, Burkitt AN, Grayden DB (2004) An analytical model for the "large, fluctuating synaptic conductance state" typical of neocortical neurons in vivo. J Comput Neurosci 16:15975 [Journal] [PubMed] Miller P, Wang XJ (2006) Stability of discrete memory states to stochastic fluctuations in neuronal systems. Chaos 16:026109 [Journal] [PubMed] Mongillo G, Amit DJ (2001) Oscillations and irregular emission in networks of linear spiking neurons. J Comput Neurosci 11:24961 [PubMed] Morrison A, Aertsen A, Diesmann M (2007) Spiketimingdependent plasticity in balanced random networks. Neural Comput 19:143767 [Journal] [PubMed] Muresan RC, Savin C (2007) Resonance or integration? Selfsustained dynamics and excitability of neural microcircuits. J Neurophysiol 97:191130 [Journal] [PubMed] Naundorf B, Geisel T, Wolf F (2005) Action potential onset dynamics and the response speed of neuronal populations. J Comput Neurosci 18:297309 [Journal] [PubMed] Nykamp DQ, Tranchina D (2000) A population density approach that facilitates largescale modeling of neural networks: analysis and an application to orientation tuning. J Comput Neurosci 8:1950 [PubMed] Paninski L (2006) The spiketriggered average of the integrateandfire cell driven by gaussian white noise. Neural Comput 18:2592616 [Journal] [PubMed] Pfeuty B, Mato G, Golomb D, Hansel D (2005) The combined effects of inhibitory and electrical synapses in synchrony. Neural Comput 17:63370 [Journal] [PubMed] Renart A, MorenoBote R, Wang XJ, Parga N (2007) Meandriven and fluctuationdriven persistent activity in recurrent networks. Neural Comput 19:146 [Journal] [PubMed] Romani S, Amit DJ, Mongillo G (2006) Meanfield analysis of selective persistent activity in presence of shortterm synaptic depression. J Comput Neurosci 20:20117 [Journal] [PubMed] Ros E, Carrillo R, Ortigosa EM, Barbour B, Agís R (2006) Eventdriven simulation scheme for spiking neural networks using lookup tables to characterize neuronal dynamics. Neural Comput 18:295993 [Journal] [PubMed] Salinas E, Sejnowski TJ (2001) Correlated neuronal activity and the flow of neural information. Nat Rev Neurosci 2:53950 [Journal] [PubMed] Soula H, Beslon G, Mazet O (2005) Spontaneous Dynamics of Asymmetric Random Recurrent Spiking Neural Networks Neural Comput 18:6079 Tchumatchenko T, Clopath C (2014) Oscillations emerging from noisedriven steady state in networks with electrical synapses and subthreshold resonance. Nat Commun 5:5512 [Journal] [PubMed]
Tiesinga PH, Fellous JM, José JV, Sejnowski TJ (2001) Computational model of carbacholinduced delta, theta, and gamma oscillations in the hippocampus. Hippocampus 11:25174 [Journal] [PubMed] Tiesinga PH, Sejnowski TJ (2004) Rapid temporal modulation of synchrony by competition in cortical interneuron networks. Neural Comput 16:25175 [Journal] [PubMed] Wenning G, Obermayer K (2003) Activity driven adaptive stochastic resonance. Phys Rev Lett 90:120602 [Journal] [PubMed] Wu Z, Guo A, Fu X (2017) Generation of lowgamma oscillations in a GABAergic network model of the striatum. Neural Netw 95:7290 [Journal] [PubMed] Zerlaut Y, Chemla S, Chavane F, Destexhe A (2018) Modeling mesoscopic cortical dynamics using a meanfield model of conductancebased networks of adaptive exponential integrateandfire neurons. J Comput Neurosci 44:4561 [Journal] [PubMed]
