Skip to main content
SpringerLink
Log in

Function dynamics

  • Published:
Japan Journal of Industrial and Applied Mathematics Aims and scope Submit manuscript

Abstract

We show mathematical structure of the function dynamics, i.e., the dynamics of interval maps ƒn+1 = (1 − ε)ƒn +εƒ n oƒ n and clarify the types of fixed points, the self-referential structure and the hierarchical structure.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. N. Kataoka and K. Kaneko, Functional dynamics. I: Articulation process. Physica D,138 (2000), 225–250.

    Article  MATH  MathSciNet  Google Scholar 

  2. N. Kataoka and K. Kaneko, Functional dynamics. II: Syntactic structure. Submitted to Physica D.

  3. J. Nagumo and S. Sato, On a response characteristic of a mathematical neuron model. Kybernetik,10 (1972), 155–164.

    Article  Google Scholar 

  4. M. Yamaguti and M. Hata, Takagi function and its generalization. Japan J. Appl. Math.,1 (1984), 186–199.

    MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Research Institute for Mathematical Sciences, Kyoto University, 606-8502, Kyoto, Japan

    Yoichiro Takahashi

  2. Meme Media Laboratory (VBL), Faculty of Engineering, Hokkaido University, 060-0810, Sapporo, Japan

    Naoto Kataoka

  3. Department of Basic Science, Graduate School of Arts and Sciences, University of Tokyo, 153-8914, Tokyo, Japan

    Kunihiko Kaneko

  4. Division of Mathematics, Hokkaido University, 060-0810, Sapporo, Japan

    Takao Namiki

Authors
  1. Yoichiro Takahashi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Naoto Kataoka
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Kunihiko Kaneko
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Takao Namiki
    View author publications

    You can also search for this author in PubMed Google Scholar

About this article

Cite this article

Takahashi, Y., Kataoka, N., Kaneko, K. et al. Function dynamics. Japan J. Indust. Appl. Math. 18, 405–423 (2001). https://doi.org/10.1007/BF03168583

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF03168583

Key words

Search

Navigation