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Cumulant Analysis of Strange Attractors: Theory and Applications

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Recent Advances in Nonlinear Dynamics and Synchronization

Part of the book series: Studies in Computational Intelligence ((SCI,volume 254))

Abstract

The material of this chapter presents a detailed description of the theoretical background of the new so-called “Degenerated Cumulant Equations Method for Statistical Analysis of Strange Attractors”. The method is illustrated by applying the results to the analysis of concrete strange attractors of traditional interest: Lorenz, Chua, Rössler. Theoretical results are confirmed by computer simulations; it is shown how by using a limited set of the first cumulants, the PDF of the attractor components can be predicted applying orthogonal series representations or model distribution approach. Practical applications are presented through the modeling of Radio-Frequency Interferences (RFI) from digital interconnects of Laptops and Desktops computers as output signals of the strange attractors mentioned above.

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Author information

Authors and Affiliations

  1. CINVESTAV, Av. IPN #2508, Col San Pedro Zacatenco, C.P., 07360, Mexico, D.F.

    V. Kontorovich

  2. Engineering and Advanced Technology Interdisciplinary Professional Unit UPIITA-IPN, Av. IPN #2580, Col Ticoman C.P., 07340, Mexico, D.F.

    Z. Lovtchikova

Authors
  1. V. Kontorovich
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  2. Z. Lovtchikova
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Editor information

Editors and Affiliations

  1. Institute for Smart-Systems Technologies, Alpen-Adria Universität Klagenfurt , Universitätsstraße 65-67, 9020, Klagenfurt, Austria

    Kyandoghere Kyamakya  & Jean Chamberlain Chedjou  & 

  2. Lehrgebiet Informationstechnik, FernUniversität in Hagen , Universitätsstraße 27 - PRG, 58097, Hagen, Germany

    Wolfgang A. Halang  & Zhong Li  & 

  3. Lehrgebiet Kommunikationsnetze, FernUniversität in Hagen , Universitätsstraße 27 - PRG, 58097, Hagen, Germany

    Herwig Unger

  4. Institute for Nonlinear Science, University of California, San Diego , 9500 Gilman Drive, 92093-0402, La Jolla, CA, USA

    Nikolai F. Rulkov

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Kontorovich, V., Lovtchikova, Z. (2009). Cumulant Analysis of Strange Attractors: Theory and Applications. In: Kyamakya, K., Halang, W.A., Unger, H., Chedjou, J.C., Rulkov, N.F., Li, Z. (eds) Recent Advances in Nonlinear Dynamics and Synchronization. Studies in Computational Intelligence, vol 254. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04227-0_4

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  • DOI: https://doi.org/10.1007/978-3-642-04227-0_4

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-04226-3

  • Online ISBN: 978-3-642-04227-0

  • eBook Packages: EngineeringEngineering (R0)

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