Citation Relationships
| Legends: | Link to a Model | Reference cited by multiple papers |
Nicola W, Campbell SA (2013) Bifurcations of large networks of two-dimensional integrate and fire neurons. J Comput Neurosci 35:87-108 [PubMed]
| • | Mean Field Equations for Two-Dimensional Integrate and Fire Models (Nicola and Campbell, 2013) |
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] Apfaltrer F, Ly C, Tranchina D (2006) Population density methods for stochastic neurons with realistic synaptic kinetics: firing rate dynamics and fast computational methods. Network 17:373-418 [Journal] [PubMed] Brette R, Gerstner W (2005) Adaptive exponential integrate-and-fire model as an effective description of neuronal activity. J Neurophysiol 94:3637-42 [Journal] [PubMed]
Casti AR, Omurtag A, Sornborger A, Kaplan E, Knight B, Victor J, Sirovich L (2002) A population study of integrate-and-fire-or-burst neurons. Neural Comput 14:957-86 [Journal] [PubMed] Destexhe A, Mainen ZF, Sejnowski TJ (1998) Kinetic models of synaptic transmission Methods In Neuronal Modeling, Koch C:Segev I, ed. pp.1
Dhooge A, Govaerts W, Kuznetsov YA (2003) MATCONT: A MATLAB package for numerical bifurcation analysis of ODEs Acm Trans Math Softw 29:141-164 Di_bernardo M, Budd C, Champneys A, Kowalczyk P, Nordmark A, Tost G, Piiroinen P (2008) Bifurcations in non-smooth dynamical systems Siam Review 50:629-701 Dur-e-Ahmad M, Nicola W, Campbell SA, Skinner FK (2012) Network bursting using experimentally constrained single compartment CA3 hippocampal neuron models with adaptation. J Comput Neurosci 33:21-40 [Journal] [PubMed] Ermentrout GB, Terman DH (2010) Mathematical Foundations of Neuroscience Interdisciplinary Applied Mathematics, Antman SS:Marsden JE:Sirovich L:Wiggins, ed. pp.1 [Journal]
Fitzhugh R (1952) Impulses and phsyiological states in theoretical models of nerve membrane Biophysical Journal 1(6):445-466 Gerstner W, Kistler WM (2002) Spiking neuron models Hemond P, Epstein D, Boley A, Migliore M, Ascoli GA, Jaffe DB (2008) Distinct classes of pyramidal cells exhibit mutually exclusive firing patterns in hippocampal area CA3b. Hippocampus 18:411-24 [Journal] [PubMed]
Hines ML, Morse T, Migliore M, Carnevale NT, Shepherd GM (2004) ModelDB: A Database to Support Computational Neuroscience. J Comput Neurosci 17:7-11 [Journal] [PubMed] Ho EC, Zhang L, Skinner FK (2009) Inhibition dominates in shaping spontaneous CA3 hippocampal network activities in vitro. Hippocampus 19:152-65 [Journal] [PubMed] Izhikevich EM (2003) Simple model of spiking neurons. IEEE Trans Neural Netw 14:1569-72 [Journal] [PubMed]
Knight BW (2000) Dynamics of encoding in neuron populations: some general mathematical features. Neural Comput 12:473-518 [PubMed] La Camera G, Giugliano M, Senn W, Fusi S (2008) The response of cortical neurons to in vivo-like input current: theory and experiment : I. Noisy inputs with stationary statistics. Biol Cybern 99:279-301 [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] 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] Markram H, Toledo-Rodriguez M, Wang Y, Gupta A, Silberberg G, Wu C (2004) Interneurons of the neocortical inhibitory system. Nat Rev Neurosci 5:793-807 [Journal] [PubMed] MathWorks Inc (2012) (2012) MATLAB Version 7.10.0 (R2012a) Naud R, Marcille N, Clopath C, Gerstner W (2008) Firing patterns in the adaptive exponential integrate-and-fire model. Biol Cybern 99:335-47 [Journal] [PubMed] Nesse WH, Borisyuk A, Bressloff PC (2008) Fluctuation-driven rhythmogenesis in an excitatory neuronal network with slow adaptation. J Comput Neurosci 25:317-33 [Journal] [PubMed] 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] 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 Sirovich L, Omurtag A, Lubliner K (2006) Dynamics of neural populations: stability and synchrony. Network 17:3-29 [Journal] [PubMed] Strogatz SH, Mirollo RE (1991) Stability of incoherence in a population of coupled oscillators J Stat Phys 63:613-635 Tikhonov A (1952) Systems of differential equations containing small parameters in the derivatives (in Russian) Matematicheskii Sbornik (NS) 31(73):575-586 Touboul J (2008) Bifurcation analysis of a general class of nonlinear integrate-and-fire neurons. Siam Appl Math 68:1045-1079 Treves A (1993) Mean field analysis of neuronal spike dynamics. Network 4:259-284 Van Vreeswijk C, Abbott LF, Ermentrout GB (1994) When inhibition not excitation synchronizes neural firing. J Comput Neurosci 1:313-21 [PubMed] van Vreeswijk C, Hansel D (2001) Patterns of synchrony in neural networks with spike adaptation. Neural Comput 13:959-92 [PubMed] Vladimirski BB, Tabak J, O'Donovan MJ, Rinzel J (2008) Episodic activity in a heterogeneous excitatory network, from spiking neurons to mean field. J Comput Neurosci 25:39-63 [Journal] [PubMed] Vreeswijk Cv (1996) Partial synchronization in populations of pulse-coupled oscillators. Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics 54:5522-5537 [PubMed] Wu Y, Lu W, Lin W, Leng G, Feng J (2012) Bifurcations of emergent bursting in a neuronal network. PLoS One 7:e38402 [Journal] [PubMed] | Ferguson KA, Huh CY, Amilhon B, Williams S, Skinner FK (2014) Simple, biologically-constrained CA1 pyramidal cell models using an intact, whole hippocampus context. F1000Res 3:104 [Journal] [PubMed]
Ho ECY, Truccolo W (2016) Interaction between Synaptic Inhibition and Glial-Potassium Dynamics leads to Diverse Seizure Transition Modes in Biophysical Models of Human Focal Seizures J Comput Neurosci [Journal]
Visser S, Van Gils SA (2014) Lumping Izhikevich neurons EPJ Nonlinear Biomedical Physics 25(12):6 [Journal]
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