Skip to main content
SpringerLink
Log in
Book cover

Dynamic Interactions in Neural Networks: Models and Data pp 15–34Cite as

Dynamical Stability of Formation of Cortical Maps

  • Conference paper

Part of the book series: Research Notes in Neural Computing ((NEURALCOMPUTING,volume 1))

Abstract

A cortical map is a localized neural representation of the signals in the outer world. A rough map is formed under the guidance of genetic information at the initial stage of development, but it is modified and refined further by self-organization. The persent paper gives a mathematical theory of formation of a cortical map by self-organization. The theory treats both dynamic of excitation patterns and dynamics of self-organization in a neural field. This not only explains the resolution and amplification properties of a cortical map, but elucidates the dynamical stability of such a map. This explains the emergence of a microcolumnar or mosaic structure in the cerebrum.

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Amari, S. [1972]: “Learning patterns and pattern sequences by self-organizing nets of threshold elements”, IEEE Trans., C-21, 1197–1206.

    MathSciNet  Google Scholar 

  • Amari, S. [1974]: “A method of statistical neurodynamics”, Kybernetik, 14, 201–215.

    MathSciNet  MATH  Google Scholar 

  • Amari, S. [1977a]: “Neural theory of association and concept-formation”, Biol Cybernetics, 26, 175–185.

    Article  MathSciNet  MATH  Google Scholar 

  • Amari, S. [1977b]: “Dynamiics of pattern formation in lateral-inhibition type neural fields”, Biol. Cybernetics, 27, 77–87.

    Article  MathSciNet  MATH  Google Scholar 

  • Amari, S. [1980]: “Topographic organization of nerve fields”, Ball. Math. Biol., 42, 339–364.

    MathSciNet  MATH  Google Scholar 

  • Amari, S. [1983]: “Field theory of self-organizing neural nets”, IEEE Trans. SMC-13, 741–748.

    MathSciNet  Google Scholar 

  • Amari, S. and Arbib, M. A. [1977a]: “Competition and cooperation in neural nets”, Systems Neuroscience, (J. Metzler ed.) Academic Press, 119–165.

    Google Scholar 

  • Amari, S., Yoshida, K. and Kanatani, K. [1977]: “A mathematical foundation for statistical neurodynamics”, SIAM J. App. Math., 33, 95–126.

    Article  MathSciNet  MATH  Google Scholar 

  • Amari, S, and Maginu, K. [1988]: “Statistical neurodynamics of associative memory”, 1, 63–73.

    Google Scholar 

  • Amari, S. and Takeuchi, A. [1978]: “Mathematical theory on formation of category detecting nerve cells”, Biol. Cybernetics, 29, 127–136.

    Article  MathSciNet  MATH  Google Scholar 

  • Arbib, M. A. [1988]: “Interacting subsystems for depth perception in the frog”, this volume.

    Google Scholar 

  • Caianiello, E. R. [1961]: “Outline of a theory of thought processes and thinking machines”, J. Theor. Biol., 1, 204–235.

    Article  MathSciNet  Google Scholar 

  • Cohen, M. and Grossberg, S. [1983]: “Absolute stability of global pattern formation and parallel memory storage by competitive neural networks” IEEE Trans., SMC-13, 815–826.

    MathSciNet  Google Scholar 

  • Cooper, L. N., Lieberman, F. and Oja, E. [1979]: “A theory for the acquisition and loss of neuron specificity in visual cortex. Biol. Cybern., 33, 9–28.

    Article  MATH  Google Scholar 

  • Fukushima, K. [1975]: “Cognition: a self-organizing multilayered network”, Biol. Cybern., 20, 121–136.

    Article  Google Scholar 

  • Haken, H. [1979]: “Synergetics, An Introduction”, 2nd enlarged ed., Berlin, Germany: Springer.

    Google Scholar 

  • Kishimoto, K. and Amari, S. [1979]: “Existence and Stability of Local Excitations in Homogeneous Neural Fields”, J. Math. Biology, 7, 303–318.

    Article  MathSciNet  MATH  Google Scholar 

  • Kohonen, T. [1982]: “Self-organized formation of topologically correct feature maps”, Biol. Cybern., 43, 59–69.

    Article  MathSciNet  MATH  Google Scholar 

  • Merzenich, M. M. [1987]: “Dynamic neocortical processes and the origins of higher brain functions”, in The Neural and Molecular Bases of Learning, eds. Changeux, J.-P. and Konishi, M., Dahlem Conference 38: Wiley.

    Google Scholar 

  • Overton, K. J. and Arbib, M. A. [1982]: “Systems matching and topographic maps: The branch-arrow model (BAM)”, in Competition and Cooperation in Neural Nets, Amari, S. and Arbib, M. A. eds., Lecture Notes in Bilmathematics, 45. Berlin, Germany: Springer.

    Google Scholar 

  • Spinelli, D. N. [1970]: “OCCAM: a computer model for a content addressable memory in the central neurons system”, in Biology of Memory, Pribram, K. M. and Broadbent, D. E. eds., Academic Press, 293–306.

    Google Scholar 

  • Takeuchi, A. and Amari, S. [1979]: “Formation of topographic maps and columnar microstructures”, Biol. Cybern., 35, 63–72.

    Article  MathSciNet  MATH  Google Scholar 

  • von der Malsburg, C. [1973]: “Self-organization of orientation sensitive cells in the striate cortex”, Kybernetik, 14, 85–100.

    Article  Google Scholar 

  • Willshaw, D. J. nad von der Malsburg, C. [1976]: “How patterned neural connections can be set up by silf-organization”, Proc. Roy. Soc., B-194, 431–445

    Google Scholar 

  • Wilson, H. R. and Cowan, J. D. [1973]: “A mathematical theory for the functional dynamics of cortical and thalamic nervous tissues”, Kybernetik, 12, 1–24.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Faculty of Engineering, University of Tokyo, Tokyo, Japan

    Shun-ichi Amari

Authors
  1. Shun-ichi Amari
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Center for Neural Engineering, University of Southern California, Los Angeles, CA, 90089-0782, USA

    Michael A. Arbib

  2. Department of Mathematical Engineering and Instrumentation Physics, University of Tokyo, Tokyo, 113, Japan

    Shun-ichi Amari

Rights and permissions

Reprints and permissions

Copyright information

© 1989 Springer-Verlag New York Inc.

About this paper

Cite this paper

Amari, Si. (1989). Dynamical Stability of Formation of Cortical Maps. In: Arbib, M.A., Amari, Si. (eds) Dynamic Interactions in Neural Networks: Models and Data. Research Notes in Neural Computing, vol 1. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-4536-0_2

Download citation

  • DOI: https://doi.org/10.1007/978-1-4612-4536-0_2

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-0-387-96893-3

  • Online ISBN: 978-1-4612-4536-0

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation