Advertisement

Modelling of Chaotic Systems with Recurrent Least Squares Support Vector Machines Combined with Stationary Wavelet Transform

  • Jiancheng Sun
  • Lun Yu
  • Guang Yang
  • Congde Lu
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3497)

Abstract

A new strategy for modeling of chaotic systems is presented, which is based on the combination of the stationary wavelet transform and Recurrent Least Squares Support Vector Machines (RLS-SVM). The stationary wavelet transform provide a sensible decomposition of the data so that the underlying temporal structures of the original time series become more tractable. The similarity of dynamic invariants between the origin and generated time series shows that the proposed method can capture the dynamics of the chaotic time series effectively.

Keywords

Support Vector Machine Lyapunov Exponent Chaotic System Correlation Dimension Strange Attractor 
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. 1.
    Brillinger, D.R.: Time series, Data Analysis and Theory. McGraw-Hill, New York (1981)zbMATHGoogle Scholar
  2. 2.
    Farmer, J.D., Sidorowich, J.J.: Predicting Chaotic Time Series. Phys. Rev. Lett. 59, 845–848 (1987)CrossRefMathSciNetGoogle Scholar
  3. 3.
    GanPcay, R.: A Statistical Framework for Testing Chaotic Dynamics Via Lyapunov Exponents. Physica D 89, 261–266 (1996)CrossRefMathSciNetGoogle Scholar
  4. 4.
    Vapnik, V.: The Nature of Statistical Learning Theory. Springer, N.Y (1995)zbMATHGoogle Scholar
  5. 5.
    Suykens, J.A.K., Van Gestel, T., De Brabanter, J., De Moor, B., Vandewalle, J.: Least Squares Support Vector Machines. World Scientific, Singapore (2002)CrossRefzbMATHGoogle Scholar
  6. 6.
    Suykens, J.A.K., Vandewalle, J.: Recurrent Least Squares Support Vector Machines. IEEE Trans. on Circuits and System-I: Fundamental Theory and Applications 47, 1109–1114 (2000)CrossRefGoogle Scholar
  7. 7.
    Kaplan, D., Glass, L.: Understanding Nonlinear Dynamics. Springer, New York (1995)zbMATHGoogle Scholar
  8. 8.
    Takens, F.: Detecting Strange Attractors in Fluid Turbulence. In: Rand, D., Young, L.S. (eds.) Dynamical systems and turbulence, Springer-Verlag, Berlin, pp. 366–381. Springer, Berlin (1981)Google Scholar
  9. 9.
    Wolf, A., Swift, J.B., Swinney, H.L., Vastano, J.A.: Determining Lyapunov Exponents from A Time Series. Physica D 16, 285–317 (1985)CrossRefzbMATHMathSciNetGoogle Scholar
  10. 10.
    Grassberger, P., Procaccia, I.: Characterization of Strange Attractors. Physical Review Letters 50, 346–349 (1983)CrossRefMathSciNetGoogle Scholar
  11. 11.
    Nason, G.P., Silverman, B.W.: The Stationary Wavelet Transform and Some Statistical Applications. In: Ledgard, H., Whiteside, J., Singer, A. (eds.) Directions in Human Factors for Interactive Systems. LNCS, vol. 103, Springer, Heidelberg (1981)Google Scholar
  12. 12.
    Weigend, A.S., Gershenfeld, N.A.: Time Series Prediction: Forecasting the Future and Understanding the Past. Addison-Wesley, Reading (1994)Google Scholar
  13. 13.
    Cao, L.: Practical Method for Determining the Minimum Embedding Dimension of a Scalar Time Series. Physica D 110, 43–50 (1997)CrossRefzbMATHGoogle Scholar
  14. 14.
    Fraser, A.M., Swinney, H.L.: Independent Coordinates for Strange Attractors from Mutual Information. Phys. Rev. A 33, 1134–1140 (1986)CrossRefzbMATHMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Jiancheng Sun
    • 1
  • Lun Yu
    • 1
  • Guang Yang
    • 2
  • Congde Lu
    • 3
  1. 1.College of Physics and Information EngineeringFuzhou UniversityFuzhouChina
  2. 2.Department of communication EngineeringXi’an Institute of Posts and TelecommunicationsXi’anChina
  3. 3.Department of Information and Communication EngineeringXi’an Jiaotong UniversityXi’anChina

Personalised recommendations