Skip to main content

Networks of Chaotic Elements

  • Chapter
  • 434 Accesses

Abstract

As an example of the high-dimensional dynamics discussed in Chap. 1, let us consider a network of chaotic elements. In a network system many elements that can display chaotic dynamics interact with each other and evolve in time. Here we introduce the globally coupled map (GCM) as the simplest example of such a network of chaotic elements. We discuss the observed phenomena and th e universal concepts revealed therein in some detail, since the model provides us with a ‘dynamic many-to-many relationship’, ‘constructive model’, and ‘dynamics between the whole and its parts’. We believe that through the study of the GCM, we can work towards a methodology studying complex systems.

Keywords

  • Lyapunov Exponent
  • Spin Glass
  • Collective Dynamic
  • Lyapunov Spectrum
  • Information Cascade

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • DOI: 10.1007/978-3-642-56861-9_4
  • Chapter length: 55 pages
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
eBook
USD   109.00
Price excludes VAT (USA)
  • ISBN: 978-3-642-56861-9
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book
USD   139.99
Price excludes VAT (USA)
Hardcover Book
USD   149.99
Price excludes VAT (USA)

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and Permissions

Copyright information

© 2001 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Kaneko, K., Tsuda, I. (2001). Networks of Chaotic Elements. In: Complex Systems: Chaos and Beyond. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-56861-9_4

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-56861-9_4

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-63132-0

  • Online ISBN: 978-3-642-56861-9

  • eBook Packages: Springer Book Archive