Interactive Exploration of Dynamical Systems

Information

• Publication Type: Technical Report
• Workgroup(s)/Project(s): not specified
• Date: January 1995
• Number: TR-186-2-95-1
• Keywords: dynamical system, interactive analysis, phase space, bifurcation, chaos theory

Abstract

Nonlinear deterministic dynamical systems often exhibit complex and chaotic behavior which is difficult to comprehend. Visualizing the characteristics of such systems is therefore essential for an understanding of the underlying dynamics. In this paper concepts for the interactive graphical exploration of analytically defined dynamical systems are discussed. Emphasis is put on interactivity which shall facilitate the investigation and exploration of such systems. The following topics on dynamical systems are treated in more detail: interactive specification, simple and fast graphical representation, and interactive modification. The paper concentrates on 2D and 3D orthographic projections of higher-dimensional phase spaces and on the display of bifurcation diagrams. A prototype software system which incorporates the previously presented ideas is shortly discussed. The software system is intended to offer a quick insight into the dynamics of a dynamical system and to enable fast investigation of variations of a dynamical system.

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BibTeX

@techreport{Groeller-1995-IED,
  title =      "Interactive Exploration of Dynamical Systems",
  author =     "Eduard Gr\"{o}ller",
  year =       "1995",
  abstract =   "Nonlinear deterministic dynamical systems often exhibit
               complex and chaotic behavior which is difficult to
               comprehend. Visualizing the characteristics of such systems
               is therefore essential for an understanding of the
               underlying dynamics. In this paper concepts for the
               interactive graphical exploration of analytically defined
               dynamical systems are discussed. Emphasis is put on
               interactivity which shall facilitate the investigation and
               exploration of such systems. The following topics on
               dynamical systems are treated in more detail: interactive
               specification, simple and fast graphical representation, and
               interactive modification. The paper concentrates on 2D and
               3D orthographic projections of higher-dimensional phase
               spaces and on the display of bifurcation diagrams. A
               prototype software system which incorporates the previously
               presented ideas is shortly discussed. The software system is
               intended to offer a quick insight into the dynamics of a
               dynamical system and to enable 		fast investigation of
               variations of a dynamical system.",
  month =      jan,
  number =     "TR-186-2-95-1",
  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 =   "dynamical system, interactive analysis, phase space,
               bifurcation, chaos theory",
  URL =        "https://www.cg.tuwien.ac.at/research/publications/1995/Groeller-1995-IED/",
}