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Time-Delayed Neural Networks: Stability and Oscillations

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Encyclopedia of Computational Neuroscience

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Definition

A time-delayed neural network is a model for a biological or artificial neural network which is formulated in terms of a delay differential equation, i.e., an equation relating the derivative of the state of the system to the state of the system at some past times. Time delays can have profound effect on the network behavior; in particular, they can induce nonlinear transient or steady-state oscillations.

Detailed Description

Biological Background

In biological neural networks, if the axon is thick and myelinated, then the transportation of signals is fast. However, a considerable portion of the axons (estimated range: 20–40 percent) are very fine myelinated fibers or unmyelinated ones. These axons play quite an important role since they give rise to long delays, up to 100–200 ms (Herz et al. 1989; Miller 1994; Swadlow and Waxman 2012). In addition, there may be (post)synaptic delays, so that long-term potentiation even occurs if the signal from the source neuron has...

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Author information

Authors and Affiliations

  1. Department of Mathematics and Statistics, York University, Toronto, ON, Canada

    Jianhong Wu

  2. Department of Applied Mathematics, University of Waterloo, Waterloo, ON, Canada

    Sue Ann Campbell

  3. Département de Mathématiques et de Statistique, Université de Montréal, QC, Canada

    Jacques Bélair

Authors
  1. Jianhong Wu
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  2. Sue Ann Campbell
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  3. Jacques Bélair
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Corresponding author

Correspondence to Jianhong Wu .

Editor information

Editors and Affiliations

  1. Atlanta, GA, USA

    Dieter Jaeger

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

    Ranu Jung

Section Editor information

  1. W.M. Keck Science Center, The Claremont Colleges, Claremont, CA, USA

    John Milton

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Wu, J., Campbell, S.A., Bélair, J. (2018). Time-Delayed Neural Networks: Stability and Oscillations. In: Jaeger, D., Jung, R. (eds) Encyclopedia of Computational Neuroscience. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-7320-6_513-2

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  • DOI: https://doi.org/10.1007/978-1-4614-7320-6_513-2

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  • Print ISBN: 978-1-4614-7320-6

  • Online ISBN: 978-1-4614-7320-6

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Chapter history

  1. Latest

    Time-Delayed Neural Networks: Stability and Oscillations
    Published:
    11 July 2018

    DOI: https://doi.org/10.1007/978-1-4614-7320-6_513-2

  2. Original

    Time-Delayed Neural Networks: Stability and Oscillations
    Published:
    08 February 2014

    DOI: https://doi.org/10.1007/978-1-4614-7320-6_513-1

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