Advertisement

Scaling properties of spatially extended chaotic systems

  • I. G. Szendro
  • J. M. López
Article
  • 29 Downloads

Abstract.

We investigate the scaling properties of Lyapunov eigenvectors and exponents in coupled-map lattices exhibiting space-time chaos. A deep interrelation between spatiotemporal chaos and kinetic roughening of surfaces is postulated. We show that the logarithm of unstable eigenvectors exhibits scale-invariance with roughness exponents that can be predicted by a simple scaling conjecture. We argue that these scaling properties should be generic in spatially homogeneous extended systems with local diffusive-like couplings.

Keywords

Lyapunov Exponent Chaotic System European Physical Journal Special Topic Large Lyapunov Exponent Positive Lyapunov Exponent 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. J.-P. Eckmann, D. Ruelle, Rev. Mod. Phys. 57, 617 (1985) CrossRefADSMathSciNetGoogle Scholar
  2. T. Bohr, M.H. Jensen, G. Paladin, A. Vulpiani, Dynamical Systems Approach to Turbulence (Cambridge University Press, Cambridge, 1998) Google Scholar
  3. A. Pikovsky, J. Kurths, Phys. Rev. E 49, 898 (1994) CrossRefADSMathSciNetGoogle Scholar
  4. A. Pikovsky, A. Politi, Nonlinearity 11, 1049 (1998) zbMATHCrossRefADSMathSciNetGoogle Scholar
  5. A. Pikovsky, A. Politi, Phys. Rev. E 63, 036207 (2001) CrossRefADSGoogle Scholar
  6. J.M. López, C. Primo, M.A. Rodríguez, I.G. Szendro, Phys. Rev. E 70, 056224 (2004) CrossRefADSGoogle Scholar
  7. A.D. Sánchez, J.M. López, M.A. Rodríguez, M.A. Matías, Phys. Rev. Lett. 92, 204101 (2004) CrossRefADSGoogle Scholar
  8. M. Kardar, G. Parisi, Y.C. Zhang, Phys. Rev. Lett. 56, 889 (1986) zbMATHCrossRefADSGoogle Scholar
  9. E. Ott, Chaos in Dynamical Systems (Cambridge University Press, Cambridge 1994) Google Scholar
  10. R. Carretero-González et al., Chaos 9, 466 (1999) CrossRefADSMathSciNetGoogle Scholar
  11. T. Bohr, G. Grinstein, C. Jayaprakash, Chaos 5, 412 (1995) CrossRefADSGoogle Scholar
  12. V. Oseledec, Trans. Moscow. Math. Soc. 19, 197 (1968) MathSciNetGoogle Scholar
  13. I. Goldhirsch, P.-L. Sulem, S.A. Orzarg, Physica D 27, 311 (1987) zbMATHCrossRefADSMathSciNetGoogle Scholar
  14. E.N. Lorenz, Proc. Seminar on Predictability (ECMRWF, Reading UK 1996) 1-18 Google Scholar

Copyright information

© EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2007

Authors and Affiliations

  • I. G. Szendro
    • 1
    • 2
  • J. M. López
    • 1
  1. 1.Instituto de Física de Cantabria (IFCA)SantanderSpain
  2. 2.Departamento de Física ModernaUniversidad de CantabriaSantanderSpain

Personalised recommendations