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Intelligent Computing Based on Chaos pp 25–51Cite as

Computational Methods for Rigorous Analysis of Chaotic Systems

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Part of the Studies in Computational Intelligence book series (SCI,volume 184)

Summary

Chaotic systems are usually studied by numerical simulations. Due to rounding errors and sensitive dependence on initial conditions simulation results may be unreliable. It is shown that computations can be done in a way that ensures that rigorous results are obtained. A set of tools for rigorous studies of nonlinear systems is presented. This includes techniques for computing enclosures of trajectories, finding and proving the existence of symbolic dynamics and obtaining rigorous bounds for the topological entropy, methods for finding accurate enclosures of chaotic attractor, interval operators for proving the existence of fixed points and periodic orbits, and methods for finding all short cycles. As illustrative examples results of a rigorous numerical analysis of the Hénon map and the Chua’s circuit are presented.

Keywords

  • Periodic Orbit
  • Chaotic System
  • Chaotic Attractor
  • Topological Entropy
  • Interval Arithmetic

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Author information

Authors and Affiliations

  1. Department of Electrical Engineering, AGH University of Science and Technology,  

    Zbigniew Galias

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  1. Zbigniew Galias
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Editors and Affiliations

  1. University of California, La Jolla, CA, USA

    Ljupco Kocarev

  2. AGH University of Science and Technology , Krakow, Poland

    Zbigniew Galias

  3. France Telecom R&D Beijing, Beijing, China

    Shiguo Lian

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Galias, Z. (2009). Computational Methods for Rigorous Analysis of Chaotic Systems. In: Kocarev, L., Galias, Z., Lian, S. (eds) Intelligent Computing Based on Chaos. Studies in Computational Intelligence, vol 184. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-95972-4_2

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  • DOI: https://doi.org/10.1007/978-3-540-95972-4_2

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