Quasidiagonal approach to the estimation of lyapunov spectra for spatiotemporal systems from multivariate time series

@article{CarreteroGonzalez2000QuasidiagonalAT,
  title={Quasidiagonal approach to the estimation of lyapunov spectra for spatiotemporal systems from multivariate time series},
  author={Carretero-Gonzalez and Orstavik and Stark},
  journal={Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics},
  year={2000},
  volume={62 5 Pt A},
  pages={6429-39}
}
We describe methods of estimating the entire Lyapunov spectrum of a spatially extended system from multivariate time-series observations. Provided that the coupling in the system is short range, the Jacobian has a banded structure and can be estimated using spatially localized reconstructions in low embedding dimensions. This circumvents the "curse of dimensionality" that prevents the accurate reconstruction of high-dimensional dynamics from observed time series. The technique is illustrated… CONTINUE READING

References

Publications referenced by this paper.
Showing 1-10 of 19 references

Theory and Applications of Coupled Map Lattices ͑John

  • K Kaneko
  • Theory and Applications of Coupled Map Lattices…
  • 1993

Dynamical Systems and Turbulence Lecture Notes in Mathematics

  • F Takens
  • Dynamical Systems and Turbulence Lecture Notes in…
  • 1981

Functional Differential Equations and Approximation of Fixed Points

  • J L Kaplan, J A Yorke
  • Lecture Notes in Mathematics
  • 1979

Chaos

  • N Parekh, V R Kumar, B D Kulkarni
  • Chaos

Commun. Math. Phys

  • D Ruelle
  • Commun. Math. Phys

IEEE Trans. Geosci. Remote Sens

  • H Leung, T Lo
  • IEEE Trans. Geosci. Remote Sens

J. Stat. Phys

  • S Lepri, A Politi, A Torcini
  • J. Stat. Phys

Nature ͑London͒

  • Y Braiman, J F Lindner, W L Ditto
  • Nature ͑London͒

Nonlinearity

  • P Collet, J.-P Eckmann
  • Nonlinearity

Phys. Lett. A

  • S O " Rstavik, J Stark
  • Phys. Lett. A

Similar Papers

Loading similar papers…