Skip to main content
SpringerLink
Log in

Simple and Complex Patterns in Coupled Map Lattices

  • Chapter
Chaos, Order, and Patterns

Part of the book series: NATO ASI Series ((NSSB,volume 280))

  • 261 Accesses

Abstract

Coupled map lattices appear mainly as a tool to understand some features of space-time motions of nonlinear spatially distributed systems and especially of turbulent flows in fluids. The last ones demonstrate two basic phenomena, i. e. space-time chaos and coherent structures. The general questions that arise in the field are:

  1. 1.

    What does it mean that the motion of a dynamic system is space-time chaotic?

  2. 2.

    What does it mean that in the motion of a dynamic system one faces coherent structures?

  3. 3.

    How could coherent structures appear from chaos?

  4. 4.

    What are the types of coexistence of these phenomena (intermittency)?

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. L. Bunimovich. Space-Time Chaos and arising of Coherent Structures in Lattices of Maps In: ”Dynamical Systems and Turbulence” (ed. by A. N. Sharcovsky), Kiev, Publ. Math. Inst. Ac. Sci. UkSSR, 1989.

    Google Scholar 

  2. L. Battiston, L. Bunimovich, R. Lima. Robust Quasihomogeneous Configurations in Coupled Map Lattices. in progress.

    Google Scholar 

  3. L. Bunimovich, A. Lambert, R. Lima. The Emergence of Coherent Structures in Coupled Map Lattices. J. of Statistical Physics, 61, (1990).

    Google Scholar 

  4. L. A. Bunimovich, Ya. G. Sinai. Space-Time Chaos in the Coupled Map Lattices. Nonlinearity. 1, (1988).

    Google Scholar 

  5. P. Collet, J.-P. Eckmann. Iterated Maps on the Interval as Dynamical Systems. Birckhäuser, Boston, 1985.

    Google Scholar 

  6. ”New Trends in Nonlinear Dynamics and Pattern Forming Phenomena” (ed. by P. Coullet, P. Huerre), Plenum, NY, 1990.

    MATH  Google Scholar 

  7. J. P. Crutchfield, K. Kaneko. Phenomenology of Spatial-Temporal Chaos. In: ”Directions in Chaos”, (ed. by Hao Bai-lin), Singapore, World Scientific, 1987, 272–353.

    Google Scholar 

  8. K. Kaneko. Pattern Dynamics In Spatial-Temporal Chaos. Physica D 34 (1986).

    Google Scholar 

  9. R. Livi, G. Martinez-Meckler, S. Ruffo. Periodic Orbits and Long Transients in Coupled Map Lattices. Physica D, (1990), to be published.

    Google Scholar 

  10. A. I. Rakhmanov, N. K. Rakhmanova. On one Dynamical System with Spatial Interactions. Preprint, Keldysh Inst. for Applied Mathem., Moscow, 1990.

    Google Scholar 

  11. D. Ruelle. Thermodynamic Formalism. London, Addison-Wesley, 1978.

    MATH  Google Scholar 

  12. Ya. G. Sinai. Gibbs Measure in Ergodic Theory. Russian Mathem. Surveys 27, (1982).

    Google Scholar 

  13. V. L. Volevich. On some Coupled Map Lattices. 1990 to be published.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute for Scientific Interchange, 10133, Torino, Italy

    L. Bunimovich

  2. Institute of Oceanology, 117218, Moscow, USSR

    L. Bunimovich

Authors
  1. L. Bunimovich
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. University of Milan, Milan, Italy

    Roberto Artuso  & Giulio Casati  & 

  2. Niels Bohr Institute, Copenhagen, Denmark

    Predrag Cvitanović

Rights and permissions

Reprints and permissions

Copyright information

© 1991 Plenum Press, New York

About this chapter

Cite this chapter

Bunimovich, L. (1991). Simple and Complex Patterns in Coupled Map Lattices. In: Artuso, R., Cvitanović, P., Casati, G. (eds) Chaos, Order, and Patterns. NATO ASI Series, vol 280. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-0172-2_9

Download citation

  • DOI: https://doi.org/10.1007/978-1-4757-0172-2_9

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4757-0174-6

  • Online ISBN: 978-1-4757-0172-2

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation