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Properties of localized oscillatory excitation in a nonlinear oscillatory field

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Abstract

We analyzed the dynamics of a nonlinear oscillatory field composed of radial isochron clocks (RICs) or Stuart-Landau (SL) oscillators, which are the simplest dynamic systems that have one stable limit cycle around one unstable equilibrium. According to our computer simulation results, the nonlinear oscillatory field with two kinds of Mexican-hat-type connection had the function of several peak detections of the external input by localized oscillatory excitation areas. Moreover, the nonlinear oscillatory field could realize in-phase phase locking within each localized oscillatory excitation area, and could maximize the phase difference between the different localized oscillatory excitation areas. As the Amari (1977) model of the nerve field provided a mathematical base for the self-organizing map (SOM) algorithm, this nonlinear oscillatory field is expected to provide a theoretical base for the oscillatory SOM algorithm.

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References

  1. Hirsch HVB, Spinelli DN (1970) Visual experience modifies distribution of horizontally and vertically oriented receptive fields in cats. Science 168:869–871

    Article  Google Scholar 

  2. Blackmore C, Cooper GF (1977) Development of the brain depends on the visual environment. Nature 228:477–478

    Article  Google Scholar 

  3. von der Malsburg C (1973) Self-organization of orientation-sensitive cells in the striate cortex. Kybernetik 14:85–100

    Article  Google Scholar 

  4. Amari S, Takeuchi A (1978) Mathematical theory on formation of category detecting nerve cells. Biol Cybern 29:127–136

    Article  MathSciNet  MATH  Google Scholar 

  5. Amari S (1977) Dynamics of pattern formation in lateral-inhibition type neural fields. Biol Cybern 27:77–87

    Article  MathSciNet  MATH  Google Scholar 

  6. Kohonen T (1995) Self-organizing maps. Springer

  7. Abbott LF, Nelson SB (2000) Synaptic plasticity: taming the beast. Nature Neurosci 3:1178–1183

    Article  Google Scholar 

  8. Eckhorn R, Bauer R, Jordan W, et al (1988) Coherent oscillations: a mechanism of feature linking in the visual cortex? Biol Cybern 60:121–130

    Article  Google Scholar 

  9. Gray CM, Konig P, Engel AK, et al (1989) Oscillatory responses in cat visual cortex exhibit intercolumnar synchronisation which reflects global stimulus properties. Nature 388:334–337

    Article  Google Scholar 

  10. Kuramoto Y (1982) Chemical oscillations, waves, and turbulence. Springer

  11. Miyata R, Date A, Kurata K (2011) Phase-locking in localized oscillatory excitation on neural oscillatory fields (in Japanese). SOFT 23(2):119–129

    Google Scholar 

  12. Hoppensteadt FC, Keener JP (1982) Phase-locking of biological clocks. J Math Biol 15(3):339–349

    Article  MathSciNet  MATH  Google Scholar 

  13. Stuart JT (1960) On the non-linear mechanics of wave disturbances in stable and unstable parallel flows Part 1. The basic behaviour in plane Poiseuille flow. J Fluid Mech 9:353–370

    Article  MathSciNet  MATH  Google Scholar 

  14. Miyata R, Kurata K (2011) Solving the binding problem with separated extraction of information by oscillatory self-organizing maps. JACIII 15(5)

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Authors and Affiliations

  1. Interdisciplinary Graduate School of Science and Engineering, Tokyo Institute of Technology, 4259-G5-17 Nagatuda-cho, Midori-ku, Yokohama, Kanagawa, 226-8502, Japan

    Ryota Miyata

  2. Faculty of Engineering, University of the Ryukyus, Okinawa, Japan

    Koji Kurata

Authors
  1. Ryota Miyata
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  2. Koji Kurata
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Correspondence to Ryota Miyata.

Additional information

This work was presented in part at the 16th International Symposium on Artificial Life and Robotics, Oita, Japan, January 27–29, 2

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Miyata, R., Kurata, K. Properties of localized oscillatory excitation in a nonlinear oscillatory field. Artif Life Robotics 16, 239–242 (2011). https://doi.org/10.1007/s10015-011-0927-7

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  • DOI: https://doi.org/10.1007/s10015-011-0927-7

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