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Analysis of Oscillatory Regimes of a Coupled Neural Oscillator System with Application to Visual Cortex Modeling

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Neural Network Dynamics

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

Abstract

A system of coupled neural oscillators is considered. A neural oscillator by Wilson-Cowan consists of a system of two nonlinear differential equations that describe the interactions between excitatory and inhibitiry populations of neurons. Oscillatory regimes of two coupled oscillators is analyzed for different connections between oscillators with particular attention to phase-locking. Bifurcation diagrams of limit cycles are computed and this allow us to describe the stability and the transformations of the oscillatory regimes. In the case of connections between excitatory populations for the small connection strengths the phase-lock mode is unstable and the anti phase oscillations are stable. Increasing connection strengths gives rise to the appearance of the stable modulated oscillations. A synchronous behavior in a chain of neural oscillators is used for simulation of experimental phenomena of stimulus-dependent assembly formation in visual cortex. The role of modulated oscillations for information processing by brain structures and binding problem are discussed.

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Author information

Authors and Affiliations

  1. Research Computing Center of the USSR Academy of Sciences, Pushchino, Moscow region, 142292, USSR

    Galina N. Borisyuk, Roman M. Borisyuk & Alexander I. Khibnik

  2. Dept. of Computer Science, Katolieke Universiteit, Leuven, B 3001, Belgium

    Alexander I. Khibnik

Authors
  1. Galina N. Borisyuk
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  2. Roman M. Borisyuk
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  3. Alexander I. Khibnik
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Editor information

Editors and Affiliations

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

    J. G. Taylor BA, BSc, MA, PhD, FlnstP (Director) (Director)

  2. Dipartimento di Fisica Teorica, Università di Salerno, Via S. Allende, 84081, Baronissi (SA), Italy

    E. R. Caianiello

  3. Department of Biophysics, The Technical University of Denmark, Building 307, DK-2800, Lyngby, Denmark

    R. M. J. Cotterill BSc, MS, PhD, DSc, FlnstP, C.Phys.

  4. Department of Physics, Washington University, St Louis, Missouri, 63130, USA

    J. W. Clark

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© 1992 Springer-Verlag London Limited

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Borisyuk, G.N., Borisyuk, R.M., Khibnik, A.I. (1992). Analysis of Oscillatory Regimes of a Coupled Neural Oscillator System with Application to Visual Cortex Modeling. In: Taylor, J.G., Caianiello, E.R., Cotterill, R.M.J., Clark, J.W. (eds) Neural Network Dynamics. Perspectives in Neural Computing. Springer, London. https://doi.org/10.1007/978-1-4471-2001-8_15

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  • DOI: https://doi.org/10.1007/978-1-4471-2001-8_15

  • Publisher Name: Springer, London

  • Print ISBN: 978-3-540-19771-3

  • Online ISBN: 978-1-4471-2001-8

  • eBook Packages: Springer Book Archive

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