Skip to main content
Springer Nature Link
Log in

Synchronization and periodic windows in a globally coupled map lattice

  • Original Article
  • Published:
Artificial Life and Robotics Aims and scope Submit manuscript

Abstract

A globally coupled map lattice (GCML) is an extension of a spin glass model. It consists of a large number of maps with a high degree of nonlinearity, and evolves iteratively under averaging interactions via their mean field. It exhibits various interesting phases in the conflict between randomness and coherence. We have found that even in its weak coupling regime, the effects of the periodic windows of element maps dominate the dynamics of the system, and the system forms periodic cluster attractors. This may give a clue to efficient pattern recognition by the brain. We analyze how the effect systematically depends on the distance from the periodic windows in the parameter space.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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

Explore related subjects

Discover the latest articles, news and stories from top researchers in related subjects.

References

  1. Kaneko K (1989) Chaotic but regular posi-nega switch among coded attractors by cluster-size variation. Phys Rev Lett 63:219–223

    Article  MathSciNet  Google Scholar 

  2. Kaneko K (1990) Globally coupled chaos violates the law of large numbers but not the central-limit theorem. Phys Rev Lett 65:1391–1394

    Article  MathSciNet  Google Scholar 

  3. Shibata T, Kaneko K (1998) Tongue-like bifurcation structures of the mean-field dynamics in a network of chaotic elements. Physica D 124:177–200

    Article  MATH  Google Scholar 

  4. Shibata T, Kaneko K (1998) Collective chaos. Phys Rev Lett 81:4116–4119

    Article  Google Scholar 

  5. Parravano AP, Cosenza MG (1999) Cluster dynamics in systems with constant mean field coupling. Int J Bifurcation Chaos 9:2311–2314

    Article  Google Scholar 

  6. Shimada T, Kikuchi K (2000) Periodicity manifestations in the turbulent regime of the globally coupled map lattice. Phys Rev E62:3489–3503

    Google Scholar 

  7. Shimada T, Kikuchi K (2001) Periodic cluster attractors and their stabilities in the turbulent globally coupled map lattice. In: Prococeedings of the International Symposium on Artificial Life and Robotics, vol 2, pp 313–316

    Google Scholar 

  8. Shimada T, Tsukada S (2002) Periodicity manifestations in the non-locally coupled maps. Physica D 168–169:126–135

    Article  Google Scholar 

  9. Perez G, Cerdeira HA (1992) Instabilities and nonstatistical behavior in globally coupled systems. Phys Rev A46:7492–7497

    Google Scholar 

  10. Metropolis N, Stein ML, Stein PR (1973) On finite limit sets for transformations on the unit interval. J Comb Theory A15:25–44

    Article  MathSciNet  Google Scholar 

  11. Kikuchi K, Shimada T (2002) Periodic window distribution in a one dimensional iterated map and its scaling relation. Trans JSCES, paper no. 20020005, pp 145–152

Download references

Author information

Authors and Affiliations

  1. Department of Physics, School of Science and Technology, Meiji University, 1-1-1 Higashimita, Tama, Kawasaki, Kanagawa, 214-8571, Japan

    Tokuzo Shimada, Kazuhiro Kubo & Takanobu Moriya

Authors
  1. Tokuzo Shimada
    View author publications

    You can also search for this author inPubMed Google Scholar

  2. Kazuhiro Kubo
    View author publications

    You can also search for this author inPubMed Google Scholar

  3. Takanobu Moriya
    View author publications

    You can also search for this author inPubMed Google Scholar

Corresponding author

Correspondence to Tokuzo Shimada.

Additional information

This work was presented in part at the 14th International Symposium on Artificial Life and Robotics, Oita, Japan, February 5–7, 2009

About this article

Cite this article

Shimada, T., Kubo, K. & Moriya, T. Synchronization and periodic windows in a globally coupled map lattice. Artif Life Robotics 14, 562–566 (2009). https://doi.org/10.1007/s10015-009-0744-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10015-009-0744-4

Key words