Biological Cybernetics

, Volume 54, Issue 2, pp 99–106 | Cite as

On the stationary state of Kohonen's self-organizing sensory mapping

  • H. Ritter
  • K. Schulten


The stationary state of the self-organizing sensory mapping of Kohonen is investigated. For this purpose the equation for the stationary state is derived for the case of one-dimensional and two-dimensional mappings. The equation can be solved for special cases, including the general one-dimensional case, to yield an explicit expression for the local magnification factor of the map.


Stationary State Explicit Expression Sensory Mapping Magnification Factor Local Magnification 
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  1. Edelman GM, Finkel LH (1985) Neuronal group selection in the cerebral cortex. In: 1st Symposium of the Neurosciences Institute, La Lolla, California, October 3–8 1982 (in press)Google Scholar
  2. Kaas JH, Merzenich MM, Killackey HP (1983) The reorganization of somatosensory cortex following peripheral nerve damage in adult and developing mammals. Annu Rev Neurosci 6:325–56Google Scholar
  3. Kohonen T (1982a) Self-organized formation of topologically correct feature maps. Biol Cybern 43:59–69Google Scholar
  4. Kohonen T (1982b) Clustering, taxonomy, and topological maps of patterns. Proceedings of the 6th International Conference on Pattern Recognition, pp 114–128Google Scholar
  5. Kohonen T (1982c) Analysis of a simple self-organizing process. Biol Cybern 44:135–140Google Scholar
  6. Kohonen T (1984) Self-organization and associative memory. Springer, Berlin Heidelberg New York TokyoGoogle Scholar
  7. Merzenich MM, Jenkins WM (1983) Dynamic maintenance and alterability of cortical maps in adults; some implications. In: Klinke R, Hartmann R (eds) Hearing — Physiological Bases and Psychophysics. Springer, Berlin Heidelberg New York TokyoGoogle Scholar
  8. Pickles JO (1982) An introduction to the physiology of hearing. Academic Press, New YorkGoogle Scholar
  9. Suga N, O'Neill WE (1979) Neural axis representing target range in the auditory cortex of the mustache bat. Science 206:351–353Google Scholar
  10. Takeuchi A, Amari S (1979) Formation of topographic maps and columnar microstructures. Biol Cybern 35:63–72Google Scholar
  11. Whitteridge D (1973) Projection of optic pathways to the visual cortex. In: Jung R (ed) Visual centers in the brain. Springer, Berlin Heidelberg New York (Handbook of sensory physiology, vol. VII/3B, pp 247–268)Google Scholar
  12. Willshaw DJ, Malsburg C von der (1976) How patterned neural connections can be set up by self-organization. Proc R Soc Lond Ser B 194:431–445Google Scholar
  13. Willshaw DJ, Malsburg C von der (1979) A marker induction mechanism for the establishment of ordered neural mappings: its application to the retinotectal problem. Proc R Soc Lond Ser B 287:203–243Google Scholar

Copyright information

© Springer-Verlag 1986

Authors and Affiliations

  • H. Ritter
    • 1
  • K. Schulten
    • 1
  1. 1.Department of PhysicsTechnical University of MunichGarchingFederal Republic of Germany

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