Encyclopedia of Computational Neuroscience

2015 Edition
| Editors: Dieter Jaeger, Ranu Jung

Integrate and Fire Models, Deterministic

Reference work entry
DOI: https://doi.org/10.1007/978-1-4614-6675-8_148



The integrate-and-fire (IF) model is a single-compartment model describing the subthreshold dynamics of the neuron membrane potential V. The spiking dynamics is marked by a spiking threshold, potential at which the neuron emits a spike. After spike emission, V is set at the neuron’s reset potential. Subthreshold dynamics was initially designed to capture neuron’s passive membrane properties, and its dynamics was given by a single first-order linear differential equation.

Variations around this model have been introduced to describe either spike-activated currents, more complex subthreshold dynamics, or more realistic spike initiation dynamics. These models can be two or three dimensional or include nonlinear terms. However, they are always designed to describe the relevant mechanisms with a minimal set of variables and parameters which make...

This is a preview of subscription content, log in to check access.


  1. Brette R, Gerstner W (2005) Adaptive exponential integrate-and-fire model as an effective description of neuronal activity. J Neuro-physiol 94(5):3637–3642Google Scholar
  2. Eccles JC (1957) The physiology of nerve cells. John Hopkins University Press, BaltimoreGoogle Scholar
  3. Ermentrout GB (1996) Type I membranes, phase resetting curves, and synchrony. Neural Comput 8:979–1001PubMedGoogle Scholar
  4. Ermentrout GB, Kopell N (1986) Parabolic bursting in an excitable system coupled with a slow oscillation. SIAM J Appl Math 46:233–253Google Scholar
  5. Fourcaud-Trocmé N, Hansel D, van Vreeswijk C, Brunel N (2003) How spike generation mechanisms determine the neuronal response to fluctuating inputs. J Neurosci 23(37):11628–11640PubMedGoogle Scholar
  6. Hutcheon B, Yarom Y (2000) Resonance, oscillation and the intrinsic frequency preferences of neurons. Trends Neurosci 23:216–222PubMedGoogle Scholar
  7. Izhikevich EM (2001) Resonate-and-fire neurons. Neural Netw 14(6–7):883–894PubMedGoogle Scholar
  8. Izhikevich EM (2003) Simple model of spiking neurons. IEEE Trans Neural Netw 14(6):1569–1572PubMedGoogle Scholar
  9. Knight BW (1972) The relationship between the firing rate of a single neuron and the level of activity in a population of neurons. J Gen Physiol 59:767–778PubMedCentralPubMedGoogle Scholar
  10. Lapicque L (1907) Recherches quantitatives sur l’excitation électrique des nerfs traitée comme une polarisation. J Physiol Paris 9:620–635Google Scholar
  11. Richardson M, Brunel N, Hakim V (2003) From subthreshold to firing-rate resonance. J Neurophysiol 89:2538–2554PubMedGoogle Scholar
  12. Treves A (1993) Mean-field analysis of neuronal spike dynamics. Network 4:259–284Google Scholar
  13. Tuckwell HC (1988) Introduction to theoretical neurobiology. Cambridge University Press, CambridgeGoogle Scholar
  14. Wang XJ, Buzśaki G (1996) Gamma oscillation by synaptic inhibition in a hippocampal interneuronal network model. J Neurosci 16:6402–6413PubMedGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Center for Research in Neuroscience of Lyon, CNRS UMR5292 - INSERM U1028Université Lyon 1LyonFrance