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Characteristics of the Chen Attractor

  • Conference paper
Nostradamus 2013: Prediction, Modeling and Analysis of Complex Systems

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 210))

Abstract

Within the paper a mathematical representation of the so-called Chen model is described as a particular parametric three-dimensional chaotic dynamical system, i.e. a system of three nonlinear differential equations evolving in time. The main aim of this paper is to find for the Chen system the properties that are known for the Lorenz system and its famous Lorenz attractor. First, the integrals of motion are derived for some parameters of the Chen system. The integrals of motions play an important role in physics, e.g. for conservation laws. Next, the shape of the global attractor of this system is approximated by volumes that contain the attractor. The shape predicts the future behavior of the system. To obtain these results, the already proved fact that the Chen system is a continued transition of the Lorenz system is used. According to our knowledge, the same approach of shifting the known facts about the Lorenz system to a newdynamical system, the Chen system in this context, has not been presented yet.

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Author information

Authors and Affiliations

  1. Institute of Information Theory and Automation of the Academy of Sciences of the Czech Republic, Pod VodáLarenskou věží 8, CZ-182 08, Prague 8, Czech Republic

    Petra Augustová & Zdeněk Beran

Authors
  1. Petra Augustová
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  2. Zdeněk Beran
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Corresponding author

Correspondence to Petra Augustová .

Editor information

Editors and Affiliations

  1. Faculty of Electrical Eng. & Comp. Sci, Department of Computer Science, VŠB-TUO, 17. listopadu 15, Ostrava-Poruba, 708 33, Czech Republic

    Ivan Zelinka

  2. , Department of Electronic Engineering, City University of Hong Kong, 83 Tat Chee Avenue, Kowloon, China, People's Republic

    Guanrong Chen

  3. , Institute of Physical, University of Tuebingen, Auf der Morgenstelle 8, Tuebingen, 72076, Germany

    Otto E. Rössler

  4. Faculty of Electrical Eng. & Comp. Sci., Department of Computer Science, VŠB-TUO, 17. listopadu 15, Ostrava-Poruba, 708 33, Czech Republic

    Vaclav Snasel

  5. (MIR Labs), Scientific Network for Innovation, Machine Intelligence Research Labs, Auburn, 98071, Washington, USA

    Ajith Abraham

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© 2013 Springer International Publishing Switzerland

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Augustová, P., Beran, Z. (2013). Characteristics of the Chen Attractor. In: Zelinka, I., Chen, G., Rössler, O., Snasel, V., Abraham, A. (eds) Nostradamus 2013: Prediction, Modeling and Analysis of Complex Systems. Advances in Intelligent Systems and Computing, vol 210. Springer, Heidelberg. https://doi.org/10.1007/978-3-319-00542-3_31

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  • DOI: https://doi.org/10.1007/978-3-319-00542-3_31

  • Publisher Name: Springer, Heidelberg

  • Print ISBN: 978-3-319-00541-6

  • Online ISBN: 978-3-319-00542-3

  • eBook Packages: EngineeringEngineering (R0)

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