Advertisement

Pramana

, Volume 64, Issue 3, pp 381–387 | Cite as

Local dimension and finite time prediction in coupled map lattices

  • P. Muruganandam
  • G. Francisco
Article

Abstract

Forecasting, for obvious reasons, often become the most important goal to be achieved. For spatially extended systems (e.g. atmospheric system) where the local nonlinearities lead to the most unpredictable chaotic evolution, it is highly desirable to have a simple diagnostic tool to identify regions of predictable behaviour. In this paper, we discuss the use of the bred vector (BV) dimension, a recently introduced statistics, to identify the regimes where a finite time forecast is feasible. Using the tools from dynamical systems theory and Bayesian modelling, we show the finite time predictability in two-dimensional coupled map lattices in the regions of low BV dimension.

Keywords

Coupled map lattices spatio-temporal chaos 

PACS Nos

05.45.Jn 05.45.Ra 05.45.Tp 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    D J Patil, B R Hunt, E Kalnay, J A Yorke and E Ott,Phys. Rev. Lett. 86, 5878 (2001)CrossRefADSGoogle Scholar
  2. [2]
    R A Johnson and D W Wichern,Applied multivariate statistical analysis (Prentice Hall, New Jersey, 1998)Google Scholar
  3. [3]
    T Bohr and O B Christensen,Phys. Rev. Lett. 63, 2161 (1989)CrossRefADSMathSciNetGoogle Scholar
  4. [4]
    H Kantz and T Schreiber,Nonlinear time series analysis (Cambridge University Press, Cambridge, 1997)MATHGoogle Scholar
  5. [5]
    N Gershenfeld,Nature of mathematical modeling (Cambridge University Press, Cambridge, 1999)MATHGoogle Scholar
  6. [6]
    H D I Abarbanel, R Brown and M B Kennel,Int. J. Mod. Phys. B5, 1347 (1991)ADSGoogle Scholar
  7. [7]
    H D I Abarbanel, R Brown and M B Kennel,J. Nonlinear Sci. 1, 175 (1991)MATHCrossRefMathSciNetGoogle Scholar
  8. [8]
    J Kurths and A Brandenburg,Phys. Rev. A44, R3427 (1991)ADSGoogle Scholar
  9. [9]
    S Yoden and M Nomura,J. Atmos. Sci. 50, 1531 (1993)CrossRefADSMathSciNetGoogle Scholar
  10. [10]
    G Francisco and P Muruganandam,Phys. Rev. E67, 066204 (2003)ADSGoogle Scholar

Copyright information

© Indian Academy of Sciences 2005

Authors and Affiliations

  • P. Muruganandam
    • 1
  • G. Francisco
    • 2
  1. 1.Department of Physics, Centre for Nonlinear DynamicsBharathidasan UniversityTiruchirapalliIndia
  2. 2.Instituto de Fýsica TeóricaUniversidade Estadual PaulistaSão Paulo-SPBrasil

Personalised recommendations