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Recent Advances in Nonlinear Dynamics and Synchronization pp 3–15Cite as

On the Construction of Dissipative Polynomial Nambu Systems with Limit Cycles

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Part of the book series: Studies in Systems, Decision and Control ((SSDC,volume 109))

Abstract

In this chapter we study nonlinear Nambu systems with canonical dissipation in four dimensions in which prescribed limit cycles arise. For this purpose we discuss some possibilities to apply concepts from the geometry of four-dimensional Euclidean spaces in order to construct a desired intersection by a set of planes and surfaces. Since scalar Nambu functions are needed for the construction of Nambu systems, the relationship between these functions and hypersurfaces will be discussed. We illustrate our considerations by means of two examples of canonical dissipative (CD) Nambu systems in which limit cycles occur. Whereas we considered the synthesis problem of limit cycle circuits with the CD Nambu approach previously, we introduce in this paper an analysis concept based on CD Nambu systems for calculating nonisolated zeros of nonlinear equations.

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Acknowledgements

We would like to thank M. Sc. Daniel Stahl and Dipl.- Ing. Marco Reit for their support with respect to Mathematica and LaTeX.

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Authors and Affiliations

  1. Technical University of Braunschweig, Braunschweig, Germany

    Richard Mathis

  2. TET, Leibniz Universität Hannover, Hanover, Germany

    Wolfgang Mathis

Authors
  1. Richard Mathis
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  2. Wolfgang Mathis
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Correspondence to Richard Mathis .

Editor information

Editors and Affiliations

  1. Lakeside Park, Alpen-Adria Universität Klagenfurt , Klagenfurt, Austria

    Kyandoghere Kyamakya

  2. Institut für Theoretische Elektrotechnik, Leibniz Universität Hannover, Hannover, Germany

    Wolfgang Mathis

  3. University of Zürich and ETH Zürich, Institute of Neuroinformatics , Zürich, Switzerland

    Ruedi Stoop

  4. Lakeside Park, Alpen-Adria Universität Klagenfurt , Klagenfurt, Austria

    Jean Chamberlain Chedjou

  5. Philipp-Reis-Gebäude, Fernuniversität Hagen , Hagen, Germany

    Zhong Li

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Mathis, R., Mathis, W. (2018). On the Construction of Dissipative Polynomial Nambu Systems with Limit Cycles. In: Kyamakya, K., Mathis, W., Stoop, R., Chedjou, J., Li, Z. (eds) Recent Advances in Nonlinear Dynamics and Synchronization. Studies in Systems, Decision and Control, vol 109. Springer, Cham. https://doi.org/10.1007/978-3-319-58996-1_1

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  • DOI: https://doi.org/10.1007/978-3-319-58996-1_1

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  • Print ISBN: 978-3-319-58995-4

  • Online ISBN: 978-3-319-58996-1

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