Skip to main content
SpringerLink
Log in

Spiking Network Models and Theory: Overview

  • Living reference work entry
  • Latest version View entry history
  • First Online:
Encyclopedia of Computational Neuroscience

  • 228 Accesses

Definition

Spiking neuronal networks are a type of neural network model where the neurons interact by sending and receiving the so-called spikes, short pulses that are only defined by their time of occurrence. Biologically, spikes correspond to the action potentials of neurons.

Neuron models that produce spikes are called spiking neuron models. Examples are the Integrate and Fire models, Deterministic; the Izhikevich model; and the Hodgkin-Huxley model.

The term spiking network was introduced to distinguish these models from formal neuron models which have graded activation functions.

Detailed Description

Historical Background

The first spiking neuron models were developed at the beginning of the twentieth century and focused on explaining the electrical behavior of isolated neurons. In 1907, Louis Lapicque proposed an electrical circuit model to describe the change in membrane potential after applying a current step. He assumed a fixed firing threshold to explain the occurrence of...

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

Access this chapter

Log in via an institution

Institutional subscriptions

References

  • Abeles M (1991) Corticonics: neural circuits of the cerebral cortex. Cambridge University Press, Cambridge

    Book  Google Scholar 

  • Bi GQ, Poo MM (1998) Synaptic modifications in cultured hippocampal neurons: dependence on spike timing, synaptic strength, and postsynaptic cell type. J Neurosci 18(24):10464–10472

    PubMed  CAS  Google Scholar 

  • Brunel N (2000) Dynamics of sparsely connected networks of excitatory and inhibitory spiking neurons. J Comput Neurosci 8(3):183–208

    Article  PubMed  CAS  Google Scholar 

  • Câteau H, Fukai T (2001) Characteristic futures of pulse packet propagation in synfire chain revealed by Fokker-Planck method. Neural Netw 14:675–685

    Article  PubMed  Google Scholar 

  • Diesmann M, Gewaltig MO, Aertsen A (1999) Stable propagation of synchronous spiking in cortical neural networks. Nature 402(6761):529–533

    Article  PubMed  CAS  Google Scholar 

  • Feldman DE (2012) The spike-timing dependence of plasticity. Neuron 75(4):556–571

    Article  PubMed  CAS  PubMed Central  Google Scholar 

  • Fuhrmann G, Segev I, Markram H, Tsodyks MV (2002) Coding of temporal information by activity-dependent synapses. J Neurophysiol 87(1):140–148

    PubMed  Google Scholar 

  • Gerstner W, Kistler WM (2002) Spiking neuron models: single neurons, populations, plasticity. Cambridge University Press, Cambridge

    Book  Google Scholar 

  • Gerstner W, Hemmen JV, Cowan J (1996a) What matters in neuronal locking? Neural Comput 8:1653–1676

    Article  PubMed  CAS  Google Scholar 

  • Gerstner W, Kempter R, van Hemmen J, Wagner H (1996b) A neuronal learning rule for sub-millisecond temporal coding. Nature 383(6595):76–78

    Article  PubMed  CAS  Google Scholar 

  • Griffith JS (1963) On the stability of brain-like structures. Biophys J 3:299–308

    Article  PubMed  CAS  PubMed Central  Google Scholar 

  • Grossberg S, Versace M (2008) Spikes, synchrony, and attentive learning by laminar thalamocortical circuits. Brain Res 1218:278–312

    Article  PubMed  CAS  Google Scholar 

  • Hill A (1936) Excitation and accommodation in nerve. Proc R Soc Lond B 814:305–355

    Article  Google Scholar 

  • Hodgkin A, Huxley A (1952) A quantitative description of membrane current and its application to conduction and excitation in nerve. J Physiol 117(4):500–544

    PubMed  CAS  PubMed Central  Google Scholar 

  • Izhikevich EM (2006) Polychronization: computation with spikes. Neural Comput 18(2):245–282

    Article  PubMed  Google Scholar 

  • Kriener B, Tetzlaff T, Aertsen A, Diesmann M, Rotter S (2008) Correlations and population dynamics in cortical networks. Neural Comput 20(9):2185–2226

    Article  PubMed  Google Scholar 

  • Lapicque L (1907) Recherches quantitatives sur l’excitation electrique des nerfs traitee comme une polarization. J Physiol Pathol Gen 9:620–635

    Google Scholar 

  • London M, Roth A, Beeren L, Hausser M, Latham PE (2010) Sensitivity to perturbations in vivo implies high noise and suggests rate coding in cortex. Nature 466(7302):123–127

    Article  PubMed  CAS  PubMed Central  Google Scholar 

  • Markram H, Lübke J, Frotscher M, Sakmann B (1997) Regulation of synaptic efficacy by coincidence of postsynaptic APs and EPSPs. Science 275:213–215

    Article  PubMed  CAS  Google Scholar 

  • Masquelier T, Thorpe SJ (2007) Unsupervised learning of visual features through spike timing dependent plasticity. PLoS Comput Biol 3(2):e31

    Article  PubMed  PubMed Central  Google Scholar 

  • Mensi S, Naud R, Pozzorini C, Avermann M, Petersen CCH, Gerstner W (2012) Parameter extraction and classification of three cortical neuron types reveals two distinct adaptation mechanisms. J Neurophysiol 107(6):1756–1775

    Article  PubMed  Google Scholar 

  • Mongillo G, Barak O, Tsodyks M (2008) Synaptic theory of working memory. Science (NY) 319(5869):1543–1546

    Article  CAS  Google Scholar 

  • Morrison A, Diesmann M, Gerstner W (2008) Phenomenological models of synaptic plasticity based on spike timing. Biol Cybern 98(6):459–478

    Article  PubMed  PubMed Central  Google Scholar 

  • Papoulis A, Pillai SU (2002) Probability, random variables and stochastic, 4th edn. McGraw-Hill, Boston

    Google Scholar 

  • Pillow JW, Shlens J, Paninski L, Sher A, Litke AM, Chichilnisky EJ, Simoncelli EP (2008) Spatio-temporal correlations and visual signalling in a complete neuronal population. Nature 454(7207):995–999

    Article  PubMed  CAS  PubMed Central  Google Scholar 

  • Plesser HE, Gerstner W (2000) Noise in integrate-and-fire neurons: from stochastic input to escape rates. Neural Comput 12(2):367–384

    Article  PubMed  CAS  Google Scholar 

  • Rajan K, Abbot LF (2006) Eigenvalue spectra of random matrices for neural networks. Phys Rev Lett 97(18):188104

    Article  PubMed  Google Scholar 

  • Sjöström J, Gerstner W (2010) Spike-timing dependent plasticity. Scholarpedia 5(2):1362

    Article  Google Scholar 

  • Stein R (1965) A theoretical analysis of neuronal variability. Biophys J 5(2):173–194

    Article  PubMed  CAS  PubMed Central  Google Scholar 

  • Sussillo D, Toyoizumi T, Maass W (2007) Self-tuning of neural circuits through short-term synaptic plasticity. J Neurophysiol 97(6):4079–4095

    Article  PubMed  Google Scholar 

  • Truccolo W, Donoghue JA, Hochberg LR, Eskandar EN, Madsen JR, Anderson WS, Brown EN, Halgren E, Cash SS (2011) Single-neuron dynamics in human focal epilepsy. Nat Neurosci 14(5):635–641

    Article  PubMed  CAS  PubMed Central  Google Scholar 

  • Tsodyks MV, Sejnowski T (1995) Rapid state switching in balanced cortical network models. Netw Comput Neural Syst 6(2):111–124

    Article  Google Scholar 

  • Tsodyks M, Pawelzik K, Markram H (1998) Neural networks with dynamic synapses. Neural Comput 10(4):821–835

    Article  PubMed  CAS  Google Scholar 

  • Tsodyks MV, Markram H, Uziel A (2000) Synchrony generation in recurrent networks with frequency-dependent synapses. J Neurosci 20(1):50

    Google Scholar 

  • Tuckwell HC (1988) Introduction to theoretical neurobiology: volume 2 nonlinear and stochastic theories. Cambridge University Press, Cambridge, UK

    Book  Google Scholar 

  • van Vreeswijk C, Sompolinsky H (1996) Chaos in neuronal networks with balanced excitatory and inhibitory activity. Science 274(5293):1724–1726

    Article  PubMed  Google Scholar 

  • Vogels T, Abbot LF (2005) Signal propagation and logic gating in networks of integrate-and-fire neurons. J Neurosci 25(46):10786–10795

    Article  PubMed  CAS  Google Scholar 

Further Reading

  • A thorough introduction to the theory of spiking networks can be found in the somewhat dated but still highly valuable textbooks Introduction to theoretical neurobiology by Tuckwell (1988). An equally thorough and more recent reference is the book Spiking neuron models: Single neurons, populations, plasticity by Gerstner and Kistler (2002) which also contains extensive treatment of learning and plasticity in spiking networks. A broader overview is given in the textbook Theoretical Neuroscience by Dayan and Abbot (2001)

    Google Scholar 

  • Burkitt AN (2006) A review of the integrate-and-fire neuron model: I. Homogeneous synaptic input. Biol Cybern 95(1):1–19

    Article  PubMed  CAS  Google Scholar 

  • Burkitt AN (2006) A review of the integrate-and-fire neuron model: II. Inhomogeneous synaptic input and network properties. Biol Cybern 95(2):97–112

    Article  PubMed  CAS  Google Scholar 

  • Burkitt (2006a, b) has written a set of comprehensive reviews of the integrate and fire neuron. The dynamic properties of spiking networks have been reviewed by Vogels et al. (2005)

    Google Scholar 

  • Dayan P, Abbot LF (2001) Theoretical neuroscience: computational and mathematical modeling of neural systems. MIT Press, Cambridge, MA

    Google Scholar 

  • Feldman (2012) provides an extensive review of spike-timing-dependent plasticity, with possible underlying synaptic and cellular mechanisms, as well as its potential role in learning. The reviews of Morrison et al. (2008) and Sjöström and Gerstner (2010) give good overview over theoretical models of spike-timing-dependent plasticity

    Google Scholar 

  • Vogels TP, Rajan K, Abbot LF (2005) Neural network dynamics. Annu Rev Neurosci 28:357–376

    Article  PubMed  CAS  Google Scholar 

Download references

Acknowledgments

This work was supported by the Blue Brain Project and EU grant FP7-269921 (BrainScaleS).

Author information

Authors and Affiliations

  1. Blue Brain Project, École Polytechnique Fédéral de Lausanne, Lausanne, 1015, Switzerland

    Dr. Marc-Oliver Gewaltig

Authors
  1. Dr. Marc-Oliver Gewaltig
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Marc-Oliver Gewaltig .

Editor information

Editors and Affiliations

  1. Atlanta, Georgia, USA

    Dieter Jaeger

  2. Department of Biomedical Engineering, Florida International University, Miami, Florida, USA

    Ranu Jung

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer Science+Business Media New York

About this entry

Cite this entry

Gewaltig, MO. (2014). Spiking Network Models and Theory: Overview. In: Jaeger, D., Jung, R. (eds) Encyclopedia of Computational Neuroscience. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-7320-6_792-3

Download citation

  • DOI: https://doi.org/10.1007/978-1-4614-7320-6_792-3

  • Received:

  • Accepted:

  • Published:

  • Publisher Name: Springer, New York, NY

  • Online ISBN: 978-1-4614-7320-6

  • eBook Packages: Springer Reference Biomedicine and Life SciencesReference Module Biomedical and Life Sciences

Publish with us

Policies and ethics

Chapter history

  1. Latest

    Spiking Network Models and Theory: Overview
    Published:
    18 September 2014

    DOI: https://doi.org/10.1007/978-1-4614-7320-6_792-3

  2. Spiking Network Models and Theory: Overview
    Published:
    01 August 2014

    DOI: https://doi.org/10.1007/978-1-4614-7320-6_792-2

  3. Original

    Spiking Network Models and Theory: Overview
    Published:
    24 March 2014

    DOI: https://doi.org/10.1007/978-1-4614-7320-6_792-1

Search

Navigation