Skip to main content
SpringerLink
Log in

Directed Network as a Chaotic Dynamical System

  • Conference paper
  • First Online:
Book cover New Frontiers in Artificial Intelligence (JSAI 2005)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 4012))

Included in the following conference series:

  • 675 Accesses

Abstract

A directed network such as the WWW can be represented by a transition matrix. Comparing this matrix to a Frobenius-Perron matrix of a chaotic piecewise-linear one-dimensional map whose domain can be divided into Markov subintervals, we are able to relate the network structure itself to chaotic dynamics. Just like various large-deviation properties of local expansion rates (finite-time Lyapunov exponents) related to chaotic dynamics, we can also discuss those properties of network structure.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Page, L., Brin, S., Motwani, R., Winograd, T.: The PageRank Citation Ranking: Bringing Order to the Web (1998), http://www-db.stanford.edu/~backrub/pageranksub.ps

  2. Mori, H., Kuramoto, Y.: Dissipative structures and chaos. Springer, Berlin (1998)

    Book  Google Scholar 

  3. Fujisaka, H., Inoue, M.: Prog. Theor. Phys. 77, 1334 (1987), Phys. Rev. A 39, 1376 (1989)

    Google Scholar 

  4. Fujisaka, H., Shibata, H.: Prog. Theor. Phys. 85, 187 (1991)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Graduate School of Informatics, Kyoto University, Kyoto, 606-8501, Japan

    Syuji Miyazaki

Authors
  1. Syuji Miyazaki
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. ISIR, Osaka University, 8-1, Mihogaoka, 567-0047, Osaka, Ibaraki, Japan

    Takashi Washio

  2. CREST, Japan Science and Technology Agency, Japan

    Akito Sakurai

  3. Dept. of Information Media, Tokyo Denki University, room 1009, 10th floor, building 11, 2-2, Kandanishikicho, Chiyodaku, 101-8457, Tokyo, Japan

    Katsuto Nakajima

  4. National Institute of Informatics, 2-1-2 Chiyoda-ku, 101-8430, Tokyo, Japan

    Hideaki Takeda

  5. Japan Advanced Institute of Science and Technology, Ishikawa, Japan

    Satoshi Tojo

  6. Department of ISEE, Kyushu University, 819-0395, Fukuoka, Japan

    Makoto Yokoo

Rights and permissions

Reprints and permissions

Copyright information

© 2006 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Miyazaki, S. (2006). Directed Network as a Chaotic Dynamical System. In: Washio, T., Sakurai, A., Nakajima, K., Takeda, H., Tojo, S., Yokoo, M. (eds) New Frontiers in Artificial Intelligence. JSAI 2005. Lecture Notes in Computer Science(), vol 4012. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11780496_29

Download citation

  • DOI: https://doi.org/10.1007/11780496_29

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-35470-3

  • Online ISBN: 978-3-540-35471-0

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation