## 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.

## Additional Files and Images

## Weblinks

No further information available.

## BibTeX

@techreport{groeller-1996-avn,
title = "Analysis and Visualization of Nonlinear Time Sequences",
author = "Anton M. Kirchsteiger and Meister 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/",
}