Biological Cybernetics

, 101:411 | Cite as

Emergence of network structure due to spike-timing-dependent plasticity in recurrent neuronal networks III: Partially connected neurons driven by spontaneous activity

  • Matthieu GilsonEmail author
  • Anthony N. Burkitt
  • David B. Grayden
  • Doreen A. Thomas
  • J. Leo van Hemmen
Original Paper


In contrast to a feed-forward architecture, the weight dynamics induced by spike-timing-dependent plasticity (STDP) in a recurrent neuronal network is not yet well understood. In this article, we extend a previous study of the impact of additive STDP in a recurrent network that is driven by spontaneous activity (no external stimulating inputs) from a fully connected network to one that is only partially connected. The asymptotic state of the network is analyzed, and it is found that the equilibrium and stability conditions for the firing rates are similar for both full and partial connectivity: STDP causes the firing rates to converge toward the same value and remain quasi-homogeneous. However, when STDP induces strong weight competition, the connectivity affects the weight dynamics in that the distribution of the weights disperses more quickly for lower density than for higher density. The asymptotic weight distribution strongly depends upon that at the beginning of the learning epoch; consequently, homogeneous connectivity alone is not sufficient to obtain homogeneous neuronal activity. In the absence of external inputs, STDP can nevertheless generate structure in the network through autocorrelation effects, for example, by introducing asymmetry in network topology.


Learning STDP Recurrent neuronal network Partial connectivity 


  1. Appleby PA, Elliott T (2006) Stable competitive dynamics emerge from multispike interactions in a stochastic model of spike-timing-dependent plasticity. Neural Comput 18(10): 2414–2464CrossRefPubMedGoogle Scholar
  2. Bi GQ, Poo MM (2001) Synaptic modification by correlated activity: Hebb’s postulate revisited. Annu Rev Neurosci 24: 139–166CrossRefPubMedGoogle Scholar
  3. Bondy A, Murty USR (2008) Graph theory. Springer, Graduate Texts in Mathematics 244Google Scholar
  4. Burkitt AN, Meffin H, Grayden DB (2004) Spike-timing-dependent plasticity: the relationship to rate-based learning for models with weight dynamics determined by a stable fixed point. Neural Comput 16(5): 885–940CrossRefPubMedGoogle Scholar
  5. Burkitt AN, Gilson M, van Hemmen JL (2007) Spike-timing-dependent plasticity for neurons with recurrent connections. Biol Cybern 96(5): 533–546CrossRefPubMedGoogle Scholar
  6. Câteau H, Kitano K, Fukai T (2008) Interplay between a phase response curve and spike-timing-dependent plasticity leading to wireless clustering. Phys Rev E 77(5): 051909CrossRefGoogle Scholar
  7. Gerstner W, Kempter R, van Hemmen JL, Wagner H (1996) A neuronal learning rule for sub-millisecond temporal coding. Nature 383(6595): 76–78CrossRefPubMedGoogle Scholar
  8. Gilson M, Burkitt AN, Grayden DB, Thomas DA, van Hemmen JL (2009a) Emergence of network structure due to spike-timing-dependent plasticity in recurrent neuronal networks I: input selectivity—strengthening correlated input pathways. Biol Cybern 101(2): 81–102CrossRefPubMedGoogle Scholar
  9. Gilson M, Burkitt AN, Grayden DB, Thomas DA, van Hemmen JL (2009b) Emergence of network structure due to spike-timing-dependent plasticity in recurrent neuronal networks II: input selectivity—symmetry breaking. Biol Cybern 101(2): 103–114CrossRefPubMedGoogle Scholar
  10. Gilson M, Burkitt AN, Grayden DB, Thomas DA, van Hemmen JL (2009c) Emergence of network structure due to spike-timing-dependent plasticity in recurrent neuronal networks IV: structuring synaptic pathways among recurrent connections. Biol Cybern. doi: 10.1007/s00422-009-0346-1
  11. Gütig R, Aharonov R, Rotter S, Sompolinsky H (2003) Learning input correlations through nonlinear temporally asymmetric Hebbian plasticity. J Neurosci 23(9): 3697–3714PubMedGoogle Scholar
  12. Hebb DO (1949) The organization of behavior: a neuropsychological theory. Wiley, New YorkGoogle Scholar
  13. Karbowski J, Ermentrout GB (2002) Synchrony arising from a balanced synaptic plasticity in a network of heterogeneous neural oscillators. Phys Rev E 65(3): 031902CrossRefGoogle Scholar
  14. Kempter R, Gerstner W, van Hemmen JL (1999) Hebbian learning and spiking neurons. Phys Rev E 59(4): 4498–4514CrossRefGoogle Scholar
  15. Levy N, Horn D, Meilijson I, Ruppin E (2001) Distributed synchrony in a cell assembly of spiking neurons. Neural Netw 14(6–7)SI:815–824Google Scholar
  16. Lubenov EV, Siapas AG (2008) Decoupling through synchrony in neuronal circuits with propagation delays. Neuron 58(1): 118–131CrossRefPubMedGoogle Scholar
  17. Masuda N, Kori H (2007) Formation of feedforward networks and frequency synchrony by spike-timing-dependent plasticity. J Comput Neurosci 22(3): 327–345CrossRefPubMedGoogle Scholar
  18. Markram H, Lübke J, Frotscher M, Roth A, Sakmann B (1997) Physiology and anatomy of synaptic connections between thick tufted pyramidal neurones in the developing rat neocortex. J Physiol (Lond) 500(2): 409–440Google Scholar
  19. Meffin H, Besson J, Burkitt AN, Grayden DB (2006) Learning the structure of correlated synaptic subgroups using stable and competitive spike-timing-dependent plasticity. Phys Rev E 73(4): 041–911CrossRefGoogle Scholar
  20. Morrison A, Aertsen A, Diesmann M (2007) Spike-timing-dependent plasticity in balanced random networks. Neural Comput 19(6): 1437–1467CrossRefPubMedGoogle Scholar
  21. Morrison A, Diesmann M, Gerstner W (2008) Phenomenological models of synaptic plasticity based on spike timing. Biol Cybern 98(6): 459–478CrossRefPubMedGoogle Scholar
  22. Pfister JP, Gerstner W (2006) Triplets of spikes in a model of spike timing-dependent plasticity Source. J Neurosci 26(38): 9673–9682CrossRefPubMedGoogle Scholar
  23. Sjöström PJ, Turrigiano GG, Nelson SB (2001) Rate, timing, and cooperativity jointly determine cortical synaptic plasticity. Neuron 32(6): 1149–1164CrossRefPubMedGoogle Scholar
  24. Song S, Abbott LF (2001) Cortical development and remapping through spike timing-dependent plasticity. Neuron 32(2): 339–350CrossRefPubMedGoogle Scholar
  25. van Rossum MCW, Bi GQ, Turrigiano GG (2000) Stable Hebbian learning from spike timing-dependent plasticity. J Neurosci 20(23): 8812–8821PubMedGoogle Scholar

Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  • Matthieu Gilson
    • 1
    • 2
    • 3
    Email author
  • Anthony N. Burkitt
    • 1
    • 2
    • 3
  • David B. Grayden
    • 1
    • 2
    • 3
  • Doreen A. Thomas
    • 1
    • 3
  • J. Leo van Hemmen
    • 4
  1. 1.Department of Electrical and Electronic EngineeringThe University of MelbourneMelbourneAustralia
  2. 2.The Bionic Ear InstituteEast MelbourneAustralia
  3. 3.NICTA, Victoria Research LabUniversity of MelbourneMelbourneAustralia
  4. 4.Physik Department (T35) and BCCN–MunichTechnische Universität MünchenGarching bei MünchenGermany

Personalised recommendations