Analysis and Visualization of Nonlinear Time Sequences

Information

• Publication Type: Technical Report
• Workgroup(s)/Project(s): not specified
• Date: January 1996
• Number: TR-186-2-96-05
• Keywords: Visualization, Time Sequences, Nonlinearity, Fractal Dimension

Abstract

During the last years there has been a considerable increase in the interest in nonlinear dynamical systems. More and more scientists apply nonlinear techniques to analyze their data sets which are often given as discrete time sequences. This paper gives a short overview on nonlinear systems and time sequences resulting from such nonlinear systems. The concept of attractors is explained and Poincare maps are described. The analysis of time sequences is discussed with respect to applying visualization techniques as steering tools in the investigation process. Because discrete time sequences resulting from measurements are typically affected by noise a signal - noise separation has to be done. The method of time delays is then subsequently used for phase-space reconstruction. Important numbers to characterize dynamical systems are fractal dimension and Lyapunov exponents. These concepts are therefore treated as well. A low cost visualization system (AVTS) was implemented which is designed to specifically support a researcher in his investigation of nonlinear time sequences. Emphasis has been put on handling of large data sets, as well as fast interactive manipulation and visual representation of time sequences. The visual inspection with AVTS allows the research to quickly focus his investigation on interesting portions of the data.

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BibTeX

@techreport{groeller-1996-avn,
  title =      "Analysis and Visualization of Nonlinear Time Sequences",
  author =     "Anton M. Kirchsteiger and Eduard Gr\"{o}ller",
  year =       "1996",
  abstract =   "During the last years there has been a considerable increase
               in the interest in nonlinear dynamical systems. More and
               more scientists apply nonlinear techniques to analyze their
               data sets which are often given as discrete time sequences.
               This paper gives a short overview on nonlinear systems and
               time sequences resulting from such nonlinear systems. The
               concept of attractors is explained and Poincare maps are
               described. The analysis of time sequences is discussed with
               respect to applying visualization techniques as steering
               tools in the investigation process. Because discrete time
               sequences resulting from measurements are typically affected
               by noise a signal - noise separation has to be done. The
               method of time delays is then subsequently used for
               phase-space reconstruction. Important numbers to
               characterize dynamical systems are fractal dimension and
               Lyapunov exponents. These concepts are therefore treated as
               well. A low cost visualization system (AVTS) was implemented
               which is designed to specifically support a researcher in
               his investigation of nonlinear time sequences. Emphasis has
               been put on handling of large data sets, as well as fast
               interactive manipulation and visual representation of time
               sequences. The visual inspection with AVTS allows the
               research to quickly focus his investigation on interesting  
                             portions of the data.",
  month =      jan,
  number =     "TR-186-2-96-05",
  address =    "Favoritenstrasse 9-11/E193-02, A-1040 Vienna, Austria",
  institution = "Institute of Computer Graphics and Algorithms, Vienna
               University of Technology ",
  note =       "human contact: technical-report@cg.tuwien.ac.at",
  keywords =   "Visualization, Time Sequences, Nonlinearity, Fractal
               Dimension",
  URL =        "https://www.cg.tuwien.ac.at/research/publications/1996/groeller-1996-avn/",
}