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Phase space reconstruction using input-output time series data.

D M Walker1, N B Tufillaro

  • 1Department of Applied Science, College of William and Mary, Williamsburg, Virginia 23187-8795, USA.

Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
|April 24, 2002
PubMed
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This study extends a method for time series analysis to determine the embedding dimension in driven systems. It offers a new diagnostic tool for complex system analysis.

Area of Science:

  • Dynamical systems theory
  • Nonlinear time series analysis
  • Chaos theory

Background:

  • Determining the embedding dimension is crucial for reconstructing the state space of dynamical systems.
  • Existing methods like false nearest neighbors (FNN) and averaged false nearest neighbors (AFNN) have limitations for driven systems.
  • Autonomous time series analysis offers potential for improved diagnostics.

Purpose of the Study:

  • To propose and evaluate an extension of Wayland et al.'s procedure for recognizing determinism in autonomous time series.
  • To utilize this extension as a diagnostic tool for determining the appropriate embedding dimension in driven (input-output) systems.
  • To compare the efficacy of this new method against established FNN and AFNN extensions.

Main Methods:

Related Experiment Videos

  • Extension of Wayland et al.'s determinism recognition procedure.
  • Application to driven time series data.
  • Comparative analysis with Rhodes and Morari's FNN extension and Cao et al.'s AFNN method.

    • Main Results:

    • The extended procedure provides a viable diagnostic for embedding dimension determination in driven systems.
    • Performance comparison with FNN and AFNN extensions highlights the strengths of the proposed method.
    • Demonstration of the method's utility in characterizing complex input-output dynamics.

    Conclusions:

    • The proposed extension offers a valuable alternative for embedding dimension selection in driven systems.
    • This approach enhances the analysis of nonlinear dynamical systems with external inputs.
    • Further research can explore its application in diverse fields of science and engineering.