Search
Menu
All issues Volume 2 / No 1 (December 2014) EPJ Nonlinear Biomed Phys, 2 1 (2014) 6 References
Issue
EPJ Nonlinear Biomed Phys
Volume 2, Number 1, December 2014
Advances in Neural Population Models and Their Networks
Article Number 6
Number of page(s) 17
DOI https://doi.org/10.1140/epjnbp19
Published online 12 May 2014
  1. Izhikevich EM: Simple model of spiking neurons.IEEE Trans Neural Netw 2003, 14:1569–1572. [Google Scholar]
  2. Izhikevich EM: Dynamical Systems in Neuroscience. Cambridge: The MIT press; 2007. [Google Scholar]
  3. Touboul J: Bifurcation analysis of a general class of nonlinear integrate-and-fire neurons.M J Appl Math 2008,68(4):1045–1079. [Google Scholar]
  4. Touboul J, Brette R: Spiking dynamics of bidimensional integrate-and-fire neurons.SIAM J Appl Dyn Syst 2009,8(4):1462–1506. [Google Scholar]
  5. Shlizerman E, Holmes P: Neural dynamics, bifurcations, and firing rates in a quadratic integrate-and-fire model with a recovery variable. i: Deterministic behavior.Neural Comput 2012,24(8):2078–2118. [Google Scholar]
  6. Wilson HR, Cowan JD: Excitatory and inhibitory interactions in localized populations of model neurons.Biophys J 1972,12(1):1–24. [Google Scholar]
  7. Wilson HR, Cowan JD: A mathematical theory of the functional dynamics of cortical and thalamic nervous tissue.Biol Cybern 1973,13(2):55–80. [Google Scholar]
  8. Lopes da Silva FH, Hoeks A, Smits H, Zetterberg LH: Model of brain rhythmic activity.Biol Cybern 1974, 15:27–37. doi:10.1007/BF00270757. [Google Scholar]
  9. Freeman WJ: Mass Action in the Nervous System. New York: Academic Press; 1975. [Google Scholar]
  10. Amari S: Dynamics of pattern formation in lateral-inhibition type neural fields.Biol Cybern 1977,27(2):77–87. [Google Scholar]
  11. Omurtag A, Knight BW, Sirovich L: On the simulation of large populations of neurons.J Comput Neurosci 2000,8(1):51–63. [Google Scholar]
  12. Nykamp DQ, Tranchina D: A population density approach that facilitates large-scale modeling of neural networks: analysis and an application to orientation tuning.J Comput Neurosci 2000,8(1):19–50. [Google Scholar]
  13. Abbott L, van Vreeswijk C: Asynchronous states in networks of pulse-coupled oscillators.Phys Rev E 1993,48(2):1483. [Google Scholar]
  14. Ly C, Tranchina D: Critical analysis of dimension reduction by a moment closure method in a population density approach to neural network modeling.Neural Comput 2007,19(8):2032–2092. [Google Scholar]
  15. Nicola W, Campbell SA: Bifurcations of large networks of two-dimensional integrate and fire neurons.J Comput Neurosci 2013,35(1):87–108. [Google Scholar]
  16. Dhooge A, Govaerts W, Kuznetsov YA: MATCONT: a MATLAB package for numerical bifurcation analysis of ODEs.ACM Trans Math Softw 2003,29(2):141–164. [Google Scholar]
  17. Bressloff PC: Spatiotemporal dynamics of continuum neural fields.J Phys A Math Theor 2011,45(3):033001. [Google Scholar]
  18. FitzHugh R: Impulses and physiological states in theoretical models of nerve membrane.Biophys J 1961,1(6):445–466. [Google Scholar]
  19. Nagumo J, Arimoto S, Yoshizawa S: An active pulse transmission line simulating nerve axon.Proc IRE 1962,50(10):2061–2070. [Google Scholar]
  20. Morris C, Lecar H: Voltage oscillations in the barnacle giant muscle fiber.Biophys J 1981,35(1):193–213. [Google Scholar]