Automatic Change Detection in Dynamical System with Chaos Based on Model, Fractal Dimension and Recurrence Plot

  • Mateusz Tykierko
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4739)


Automatic change detection is the important subject in dynamical systems. There are known techniques for linear and some techniques for nonlinear systems, but merely few of them concern deterministic chaos. This paper presents automatic change detection technique for dynamical systems with chaos based on three different approaches neural network model, fractional dimension and recurrence plot. Control charts are used as a tool for automatic change detection. We consider the dynamical system described by the univariate time series. We assume that change parameters are unknown and the change could be either slight or drastic. Methods are checked by using small data set and stream data.


Fractal Dimension Change Detection Control Chart Lorenz System Exponentially Weight Move Average 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Alon, N., Matias, Y., Szegedy, M.: The space complexity of approximating the frequency moments, pp. 20–29 (1996)Google Scholar
  2. 2.
    Falconer, K.: Fractal Geometry. Wiley, New York (1990)zbMATHGoogle Scholar
  3. 3.
    Fraser, A.M., Swinney, H.L.: Independent coordinates for strange attractors from mutual information. Phys. Review A 33 (1986)Google Scholar
  4. 4.
    Gonzalez, F., Dasgupta, D.: Anomaly detection using real-valued negative selection (2003)Google Scholar
  5. 5.
    Haykin, S.: Neural networks: a comprehensive foundation. Prentice Hall, Englewood Cliffs (1999)zbMATHGoogle Scholar
  6. 6.
    Haykin, S., Principe, J.: Making sense of complex world. IEEE Signal Process. Mag. 15, 66–81 (1998)CrossRefGoogle Scholar
  7. 7.
    Hively, L.M., Protopopescu, V.A.: Timely detection of dynamical change in scalp eeg signals. Chaos 10 (2000)Google Scholar
  8. 8.
    Ilin, A., Valpola, H.: Nonlinear dynamical factor analysis for state change detection. IEEE Trans. on Neural Network 15(3) (2004)Google Scholar
  9. 9.
    Ruelle, D., Eckmann, J.P., Kamphorst, S.O.: Recurrence plots of dynamical systems. Europhys. Lett. 4 (1987)Google Scholar
  10. 10.
    Webber Jr., C.L., Zbilut, J.P.: Dynamical assessment of physiological systems and states using recurrence plot strategies. J. Appl. Physiol. 78 (1994)Google Scholar
  11. 11.
    Kennel, M.B., Brown, R.: Determining embedding dimension for phase-space reconstruction using a geometrical construction. Phys.Rev. A 45 (1992)Google Scholar
  12. 12.
    Marwan, N.: Encounters With Neighbours - Current Developments Of Concepts Based On Recurrence Plots And Their Applications. PhD thesis (2003)Google Scholar
  13. 13.
    Montgomery, D.C.: Introduction to Statistical Quality Control, 4th edn. Wiley, Chichester (2001)Google Scholar
  14. 14.
    Orr, M.J.: Regularisation in the selection of rbf centres. Neural Computation 7(3) (1995)Google Scholar
  15. 15.
    Ott, E.: Chaos in Dynamical Systems. Cambridge University Press, Cambridge (1993)zbMATHGoogle Scholar
  16. 16.
    Principe, J.C., Rathie, A.: Prediction of chaotic time series with neural networks and the issue od dynamic modeling. International Journal of Bifurcation and Chaos (1992)Google Scholar
  17. 17.
    Sauer, T., Yorke, J.A., Casdagli, M.: Embedology. Journal Statistical Physics (1991)Google Scholar
  18. 18.
    Schuster, H.G.: Deterministic Chaos. Weinheim: VGH Verlagsgesellschaft (1988)Google Scholar
  19. 19.
    Tricot, C.: Curves and Fractal Dimension. Springer, Heidelberg (1995)zbMATHGoogle Scholar
  20. 20.
    Wong, A., Wu, L.: Fast estimation of fractal dimension and correlation integral on stream data. Inf. Process. Letters 93 (2003)Google Scholar
  21. 21.
    Wu, L., Faloutsos, C., Fracdim. Perl package (January 2001), available at

Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Mateusz Tykierko
    • 1
  1. 1.Institute of Computer Engineering,Control and Robotics, Wroclaw University of Technology, ul. Wybrzeze Wyspianskiego 27, 50-370 WroclawPoland

Personalised recommendations