Citation Relationships

Legends: Link to a Model Reference cited by multiple papers


Marpeau F, Barua A, Josic K (2009) A finite volume method for stochastic integrate-and-fire models. J Comput Neurosci 26:445-57 [PubMed]

   A finite volume method for stochastic integrate-and-fire models (Marpeau et al. 2009)

References and models cited by this paper

References and models that cite this paper

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]
Barth T, Ohlberger M (2004) Finite volume methods: Foundation and analysis Encyclopedia of computational mechanics
Bruneau CH, Marpeau F, Saad M (2005) Numerical simulation of the miscible displacement of radionuclides in a heterogeneous porous medium International Journal For Numerical Methods In Fluids 49(10):1053-1085
Brunel N, Chance FS, Fourcaud N, Abbott LF (2001) Effects of synaptic noise and filtering on the frequency response of spiking neurons. Phys Rev Lett 86:2186-9 [Journal] [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]
Brunel N, Latham PE (2003) Firing rate of the noisy quadratic integrate-and-fire neuron. Neural Comput 15:2281-306 [Journal] [PubMed]
Burkitt AN (2006) A review of the integrate-and-fire neuron model: I. Homogeneous synaptic input. Biol Cybern 95:1-19 [Journal] [PubMed]
Courant R, Friedrichs K, Lewy H (1928) Uber die partiellen differenzengleichungen der mathematischen Physik. Mathematische Annalen 100(1):32-74
Doiron B, Chacron MJ, Maler L, Longtin A, Bastian J (2003) Inhibitory feedback required for network oscillatory responses to communication but not prey stimuli. Nature 421:539-43 [Journal] [PubMed]
Ermentrout GB, Kopell N (1986) Parabolic bursting in an excitable system coupled with a slow oscillation. Siam J Appl Math 46:233-253
Galan RF, Ermentrout GB, Urban NN (2007) Stochastic dynamics of uncoupled neural oscillators: Fokker-Planck studies with the finite element method. Physical Review E 76:56110
Gardiner C (1985) Handbook of Stochastic Methods
Godlewski E, Raviart PA (1990) Hyperbolic systems of conservation laws. Mathematiques et applications
Harten A (1983) High resolution schemes for hyperbolic conservation laws Journal Of Computational Physics 49:357-392
Kloeden PE, Platen E (1992) Numerical Solution Of Stochastic Differential Equations
Lapicque L (1907) Recherches quantitatives sur lexcitation electrique des nerfs traitee comme une polarisation J Physiol Pathol Gen 9:620-635 [Journal]
Lascaux P, Theodor R () Analyse numerique matricielle appliquee à l'Art de l'Ingenieur
Latham PE, Richmond BJ, Nelson PG, Nirenberg S (2000) Intrinsic dynamics in neuronal networks. I. Theory. J Neurophysiol 83:808-27 [Journal] [PubMed]
Lindner B (2001) Coherence and stochastic resonance in nonlinear dynamical systems Ph.D. thesis
Lindner B, Longtin A (2006) Comment on "Characterization of subthreshold voltage fluctuations in neuronal membranes," by M. Rudolph and A. Destexhe. Neural Comput 18:1896-931 [Journal] [PubMed]
Lindner B, Schimansky-Geier L (2001) Transmission of noise coded versus additive signals through a neuronal ensemble. Phys Rev Lett 86:2934-7 [Journal] [PubMed]
Mattia M, Del Giudice P (2002) Population dynamics of interacting spiking neurons. Phys Rev E Stat Nonlin Soft Matter Phys 66:051917 [Journal] [PubMed]
Mattia M, Del_giudice P (2004) Finite-size dynamics of inhibitory and excitatory interacting spiking neurons Physical Review 70(5):52903
Press WH, Flannery BP, Teukolsky SA, Vetterling WT (2007) Numerical recipes: the art of scientific computing 3rd edition
Rall W (1995) The Theoretical Foundation Of Dendritic Function, Segev I:Rinzel J:Shepherd GM, ed.
Renart A, Brunel N, Wang X-J (2003) Mean-field theory of recurrent cortical networks: from irregularly spiking neurons to working memory Computational neuroscience: a comprehensive approach, Feng J, ed. pp.431
Risken H (1989) The Fokker-Planck Equation (2nd ed)
Roe PL (1984) Generalized formulation of TVD Lax-Wendroff schemes. ICASE Rep :53-84
Rudolph M, Destexhe A (2005) An extended analytic expression for the membrane potential distribution of conductance-based synaptic noise. Neural Comput 17:2301-15 [Journal] [PubMed]
   Steady-state Vm distribution of neurons subject to synaptic noise (Rudolph, Destexhe 2005) [Model]
Strang G (1968) On the construction and comparison of difference schemes Siam Journal On Numerical Analysis 5:506-517
Sweby PK (1984) High resolution schemes using flux limiters for hyperbolic conservation laws. Siam Journal On Numerical Analysis 21:995-1011
Toro EF (2001) Godunov methods: Theory and applications
Tuckwell HC (1988) Introduction To Theoretical Neurobiology: Vol 1, Linear Cable Theory And Dendritic Structure
Tuckwell HC (1989) Stochastic Processes In The Neurosciences
(34 refs)