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Theory and Applications of Neural Networks pp 198–210Cite as

Dynamics of Binary Networks with Extended Time-Summation

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Part of the book series: Perspectives in Neural Computing ((PERSPECT.NEURAL))

Abstract

A model of a binary network with extended time-summation is derived by considering a leaky integrator shunting network in which the output of each neuron is taken to be a sequence of impulses or spikes. The nature of the extended time-summation involves keeping a record of the network output activity that reaches back to some chosen initial time. It is therefore no longer possible to specify the state of the network at any particular time in terms of the discrete space of binary outputs (0, 1)N. The appropriate description of the network dynamics is now in terms of the continuous space of internal activations R N. Neural networks with extended time-summation can exhibit various forms of complex dynamics including phase-locking and chaos, in contrast to standard binary networks whose dynamics is necessarily recurrent; this is illustrated in the case of a single neuron. The effects of noise in such networks are also briefly discussed.

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Authors
  1. P. C. Bressloff
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Editors and Affiliations

  1. Department of Mathematics, King’s College, Strand, London, WC2R 2LS, UK

    J. G. Taylor BA, BSc, MA, PhD, FInstP

  2. Department of Electrical Engineering, University of Surrey, Guildford, Surrey, GU2 5XH, UK

    C. L. T. Mannion BSc, PhD, MInstP

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© 1992 Springer-Verlag London Limited

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Bressloff, P.C. (1992). Dynamics of Binary Networks with Extended Time-Summation. In: Taylor, J.G., Mannion, C.L.T. (eds) Theory and Applications of Neural Networks. Perspectives in Neural Computing. Springer, London. https://doi.org/10.1007/978-1-4471-1833-6_12

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  • DOI: https://doi.org/10.1007/978-1-4471-1833-6_12

  • Publisher Name: Springer, London

  • Print ISBN: 978-3-540-19650-1

  • Online ISBN: 978-1-4471-1833-6

  • eBook Packages: Springer Book Archive

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