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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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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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Corresponding author

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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