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Network: Computation in Neural Systems Volume 17, 2006 - Issue 1
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ORIGINAL ARTICLE

Dynamics of neural populations: Stability and synchrony

Lawrence Sirovich Laboratory of Applied Mathematics, Mount Sinai School of Medicine, 1 Gustave L. Levy Place, New York, NY, 10029, USA
,
Ahmet Omurtag Laboratory of Applied Mathematics, Mount Sinai School of Medicine, 1 Gustave L. Levy Place, New York, NY, 10029, USA
&
Kip Lubliner Laboratory of Applied Mathematics, Mount Sinai School of Medicine, 1 Gustave L. Levy Place, New York, NY, 10029, USA
Pages 3-29 | Received 24 Feb 2005, Accepted 19 Oct 2005, Published online: 09 Jul 2009

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JoséA. Carrillo, Maríad. M. González, MariaP. Gualdani & MariaE. Schonbek. (2013) Classical Solutions for a Nonlinear Fokker-Planck Equation Arising in Computational Neuroscience. Communications in Partial Differential Equations 38:3, pages 385-409.
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Jian-Guo Liu, Ziheng Wang, Yuan Zhang & Zhennan Zhou. (2022) Rigorous Justification of the Fokker--Planck Equations of Neural Networks Based on an Iteration Perspective. SIAM Journal on Mathematical Analysis 54:1, pages 1270-1312.
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Jeongho Kim, Benoît Perthame & Delphine Salort. (2020) Fast Voltage Dynamics of Voltage–Conductance Models for Neural Networks. Bulletin of the Brazilian Mathematical Society, New Series 52:1, pages 101-134.
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Dipty Sharma & Paramjeet Singh. (2020) Discontinuous Galerkin approximation for excitatory-inhibitory networks with delay and refractory periods. International Journal of Modern Physics C 31:03, pages 2050041.
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Santosh Kumar & Paramjeet Singh. (2019) High order WENO finite volume approximation for population density neuron model. Applied Mathematics and Computation 356, pages 173-189.
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Dipty Sharma, Paramjeet Singh, Ravi P. Agarwal & Mehmet Emir Koksal. (2019) Numerical Approximation for Nonlinear Noisy Leaky Integrate-and-Fire Neuronal Model. Mathematics 7:4, pages 363.
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Nicholas Cain, Ramakrishnan Iyer, Christof Koch & Stefan Mihalas. (2016) The Computational Properties of a Simplified Cortical Column Model. PLOS Computational Biology 12:9, pages e1005045.
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Hasan Onur Keles, Randall L. Barbour & Ahmet Omurtag. (2016) Hemodynamic correlates of spontaneous neural activity measured by human whole-head resting state EEG + fNIRS. NeuroImage 138, pages 76-87.
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Julien Chevallier, María José Cáceres, Marie Doumic & Patricia Reynaud-Bouret. (2015) Microscopic approach of a time elapsed neural model. Mathematical Models and Methods in Applied Sciences 25:14, pages 2669-2719.
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William W Lytton, Samuel A Neymotin & Cliff C Kerr. (2014) Multiscale modeling for clinical translation in neuropsychiatric disease. Journal of Computational Surgery 1:1.
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A. Rothkegel & K. Lehnertz. (2014) Synchronization in populations of sparsely connected pulse-coupled oscillators. EPL (Europhysics Letters) 105:3, pages 30003.
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Grégory Dumont, Jacques Henry & Carmen Tarniceriu. (2014) A Density Model for a Population of Theta Neurons. The Journal of Mathematical Neuroscience 4:1, pages 2.
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Grégory Dumont & Jacques Henry. (2012) Population density models of integrate-and-fire neurons with jumps: well-posedness. Journal of Mathematical Biology 67:3, pages 453-481.
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Wilten Nicola & Sue Ann Campbell. (2013) Bifurcations of large networks of two-dimensional integrate and fire neurons. Journal of Computational Neuroscience 35:1, pages 87-108.
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Grégory Dumont & Jacques Henry. (2013) Synchronization of an Excitatory Integrate-and-Fire Neural Network. Bulletin of Mathematical Biology 75:4, pages 629-648.
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María J Cáceres, José A Carrillo & Benoît Perthame. (2011) Analysis of Nonlinear Noisy Integrate&Fire Neuron Models: blow-up and steady states. The Journal of Mathematical Neuroscience 1:1, pages 7.
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Chin-Yueh Liu & Duane Q. Nykamp. (2008) A kinetic theory approach to capturing interneuronal correlation: the feed-forward case. Journal of Computational Neuroscience 26:3, pages 339-368.
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Alexander Rothkegel & Klaus Lehnertz. (2009) Multistability, local pattern formation, and global collective firing in a small-world network of nonleaky integrate-and-fire neurons. Chaos: An Interdisciplinary Journal of Nonlinear Science 19:1.
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Raul VicenteLeonardo L. GolloClaudio R. MirassoIngo FischerGordon Pipa. (2008) Dynamical relaying can yield zero time lag neuronal synchrony despite long conduction delays. Proceedings of the National Academy of Sciences 105:44, pages 17157-17162.
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Marc de Kamps, Volker Baier, Johannes Drever, Melanie Dietz, Lorenz Mösenlechner & Frank van der Velde. (2008) The state of MIIND. Neural Networks 21:8, pages 1164-1181.
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Lawrence Sirovich. (2008) Populations of Tightly Coupled Neurons: The RGC/LGN System. Neural Computation 20:5, pages 1179-1210.
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Padmini Rangamani & Lawrence Sirovich. (2007) Survival and apoptotic pathways initiated by TNF-α: Modeling and predictions. Biotechnology and Bioengineering 97:5, pages 1216-1229.
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William W. Lytton & Ahmet Omurtag. (2007) Tonic-Clonic Transitions in Computer Simulation. Journal of Clinical Neurophysiology 24:2, pages 175-181.
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Ahmet Omurtag & Lawrence Sirovich. (2006) Modeling a large population of traders: Mimesis and stability. Journal of Economic Behavior & Organization 61:4, pages 562-576.
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Bard Ermentrout. (2006) Gap junctions destroy persistent states in excitatory networks. Physical Review E 74:3.
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