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Complex behavior of simple maps with fluctuating delay times

  • Statistical and Nonlinear Physics
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Abstract

Delay systems used to model retarded actions are relevant in many fields such as optics, mechanical machining, biology or physiology. A frequently encountered situation is that the length of the delay time changes with time. In this study, we use a simple map system to investigate the influence of the fluctuating delay time on the system dynamics. For simplicity, we start from a case with the delay time taking only the value of zero or one discrete time steps, where the system dynamics reduces to one- and two-dimensional map, respectively. We study two situations, periodic or random variation of the delay. Rich dynamics including coexisting multiple attractors, strange nonchaotic attractors and on-off intermittency are observed. For a special case we can show analytically the existence of a dense set of singularities of the Lyapunov exponent. Finally we present results for higher dimensional generalizations to show the relevance of our findings to more general situations.

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Authors and Affiliations

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

    G. Radons, H.-L. Yang, J. Wang & J.-F. Fu

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  1. G. Radons
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  2. H.-L. Yang
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  3. J. Wang
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  4. J.-F. Fu
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Correspondence to G. Radons.

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Radons, G., Yang, HL., Wang, J. et al. Complex behavior of simple maps with fluctuating delay times. Eur. Phys. J. B 71, 111–119 (2009). https://doi.org/10.1140/epjb/e2009-00262-8

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  • DOI: https://doi.org/10.1140/epjb/e2009-00262-8

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