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Dynamical Systems with Time-Varying Delay: Dissipative and More Dissipative Systems

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Complexity and Synergetics

Abstract

We investigate the dynamical properties of time-delay systems with time-varying delay, where we focus on the influence of the functional structure of the delay. Two universality classes of systems with time-varying delays are presented which lead to fundamental differences in the dynamics of the related systems, as for example the scaling behavior of the Lyapunov spectrum. The classification is connected to the well-known existence or non-existence of topological conjugacies of circle maps to constant rotations. It is independent of the specific delay system.

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Authors and Affiliations

  1. Institute of Physics, Chemnitz University of Technology, 09107, Chemnitz, Germany

    David Müller, Andreas Otto & Günter Radons

Authors
  1. David Müller
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  2. Andreas Otto
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  3. Günter Radons
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Corresponding author

Correspondence to Günter Radons .

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Editors and Affiliations

  1. Institute of Experimental Physics, Otto-von-Guericke University Magdeburg, Magdeburg, Germany

    Stefan C. Müller

  2. Department of Physical Chemistry, Fritz-Haber-Institute of the MPG, Berlin, Germany

    Peter J. Plath

  3. Institute of Physics, Complex Systems, Technical University Chemnitz, Chemnitz, Germany

    Günter Radons

  4. Center for Complex Systems and Brain Sciences, Florida Atlantic University, Boca Raton, Florida, USA

    Armin Fuchs

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Müller, D., Otto, A., Radons, G. (2018). Dynamical Systems with Time-Varying Delay: Dissipative and More Dissipative Systems. In: Müller, S., Plath, P., Radons, G., Fuchs, A. (eds) Complexity and Synergetics. Springer, Cham. https://doi.org/10.1007/978-3-319-64334-2_3

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  • DOI: https://doi.org/10.1007/978-3-319-64334-2_3

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-64333-5

  • Online ISBN: 978-3-319-64334-2

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