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An analytically solvable model of collective excitation patterns in cortical tissue

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A Perspective Look at Nonlinear Media

Part of the book series: Lecture Notes in Physics ((LNP,volume 503))

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References

  • S. I. Amari. Dynamics of pattern formation in lateral-inhibition type neural fields. Biol. Cybern., 27:77–87, 1977.

    Article  MATH  MathSciNet  Google Scholar 

  • A. Belmonte and J.-M. Flesselles. Experimental determination of the dispersion relation for spiral waves. Phys. Rev. Lett., 77(6):1174–1177, 1996.

    Article  ADS  Google Scholar 

  • G. B. Ermentrout and J. D. Cowan. A mathematical theory of visual hallucination patterns. Biol. Cybern., 34:137–150, 1979.

    Article  MATH  MathSciNet  Google Scholar 

  • C. Fohlmeister, W. Gerstner, R. Ritz, and J. L. van Hemmen. Spontaneous excitations in the visual cortex: stripes, spirals, rings, and collective bursts. Neural Comput., 7:1046–1055, 1995.

    Article  Google Scholar 

  • W. Gerstner and J. L. van Hemmen. Associative memory in a network of 'spiking’ neurons. Network, 3:139–164, 1992.

    Article  MATH  Google Scholar 

  • G. Gripenberg, S. O. Londen, and O. Staffans. Volterra integral and functional equations, volume 34 of Encyclopedia of Mathematics and Its Applications. Cambridge University Press, Cambridge MA, 1990.

    Book  MATH  Google Scholar 

  • J. P. Keener and J. J. Tyson. Spiral waves in the Belousov-Zhabotinskii reaction. Physica, 21:307–324, 1986.

    MATH  MathSciNet  Google Scholar 

  • W. M. Kistler, W. Gerstner, and J. L. van Hemmen. Reduction of the Hodgkin-Huxley equations to a single-variable threshold model. Neural Comput., 9(5):1015–1045, 1997a.

    Article  Google Scholar 

  • W. M. Kistler, R. Seitz, and J. L. van Hemmen. Modelling collective excitations in cortical tissue. Submitted to Physica D, 1997b.

    Google Scholar 

  • H. Klüver. Mescal and the mechanism of hallucinations. The University of Chicago Press, Chicago, IL, 1966. This is a reprint of two papers which appeared in 1928 and 1942.

    Google Scholar 

  • J. Milton. Dynamics of small neural populations. Amer. Math. Soc., Providence, RI, 1996.

    MATH  Google Scholar 

  • G. M. Shepherd. Neurobiology. Oxford University Press, New York, 2nd edition, 1988.

    Google Scholar 

  • H. R. Wilson and J. D. Cowan. A mathematical theory of the functional dynamics of cortical and thalamic nervous tissue. Kybernetik, 13:55–80, 1973.

    Article  Google Scholar 

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Authors and Affiliations

  1. Physik Department der TU-München, D-85747, Garching bei München, Germany

    Werner M. Kistler & J. Leo van Hemmen

Authors
  1. Werner M. Kistler
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  2. J. Leo van Hemmen
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Jürgen Parisi Stefan C. Müller Walter Zimmermann

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© 1998 Springer-Verlag

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Kistler, W.M., van Hemmen, J.L. (1998). An analytically solvable model of collective excitation patterns in cortical tissue. In: Parisi, J., Müller, S.C., Zimmermann, W. (eds) A Perspective Look at Nonlinear Media. Lecture Notes in Physics, vol 503. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0104967

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  • DOI: https://doi.org/10.1007/BFb0104967

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-63995-4

  • Online ISBN: 978-3-540-69681-0

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