Hebbian delay adaptation in a network of integrate-and-fire neurons

  • Christian W. Eurich
  • Jack D. Cowan
  • John G. Milton
Part I: Coding and Learning in Biology
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1327)


We study the synchronization properties of a neural network which incorporates time delays. Two layers of integrate-and-fire neurons are connected by delay lines and a Hebbian-type learning rule is applied to allow a self-organizing, adaptive modification of the delays. It is shown that when the network synchronizes to a periodic input of period T, the delays differ by multiples of T. The delay dynamics possess an (N + 1)-parameter set of fixed points which is locally attracting. Neural networks with delay adaptation may have applications as noise reduction algorithms and for the control of time-delayed dynamical systems.


Delay Line Learning Rule Postsynaptic Neuron Interaural Time Difference Presynaptic Neuron 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Baldi, P., Atiya, A. F.: How delays affect neural dynamics and learning. IEEE Trans. Neural Networks 5 (1994) 612–621Google Scholar
  2. 2.
    Carr, C. E.: Processing of temporal information in the brain. Annu. Rev. Neurosci. 16 (1993) 223–243Google Scholar
  3. 3.
    Carr, C. E., Konishi, M.: A circuit for detection of interaural time differences in the brain stem of the barn owl. J. Neurosci. 10 (1990) 3227–3246Google Scholar
  4. 4.
    Eurich, C. W., Cowan, J. D., Milton, J. G.: A Hebbian learning rule for delay adaptation in integrate-and-fire neural networks. Preprint, submittedGoogle Scholar
  5. 5.
    Eurich, C. W., Milton, J. G.: Noise-induced transitions in human postural sway. Phys. Rev. E 54 (1996) 6681–6684Google Scholar
  6. 6.
    Gerstner, W., Kempter, R., van Hemmen, J. L., Wagner, H.: A neuronal learning rule for sub-millisecond temporal coding. Nature 383 (1996) 76–78Google Scholar
  7. 7.
    Glünder, H., Hüning, H.: Detection of spatio-temporal spike patterns by unsupervised synaptic delay learning. In: Elsner, N, Schnitzler, H.-U. (eds): Brain and Evolution. Thieme, Stuttgart (1996) 800Google Scholar
  8. 8.
    Hebb, D. O.: The Organization of Behavior. Wiley, New York (1949)Google Scholar
  9. 9.
    Markham, H., Tsodyks, M.: Redistribution of synaptic efficacy between neocortical pyramidal neurons. Nature 382 (1996) 807–810Google Scholar
  10. 10.
    Napp-Zinn, H., Jansen, M., Eckmiller, R.: Recognition and tracking of impulse patterns with delay adaptation in biology-inspired pulse-processing neural net (BNP) hardware. Biol. Cybern. 74 (1996) 449–453Google Scholar
  11. 11.
    Pyragas, K.: Continuous control of chaos in self-controlling feedback. Phys. Lett. A 170 (1992) 421–428Google Scholar
  12. 12.
    Turrigiano, G., Abbott, L. F., Marder, E.: Activity-dependent changes in the intrinsic properties of cultured neurons. Science 264 (1994) 974–977Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Christian W. Eurich
    • 1
  • Jack D. Cowan
    • 2
  • John G. Milton
    • 3
  1. 1.Institut für Theoretische PhysikUniversität BremenBremenGermany
  2. 2.Departments of Mathematics and NeurologyThe University of ChicagoChicagoUSA
  3. 3.Department of Neurology and Committee on NeurobiologyThe University of ChicagoChicagoUSA

Personalised recommendations