Complex behavior of simple maps with fluctuating delay times

Research output: Contribution to journalResearch articleContributedpeer-review


  • G. Radons - , Chemnitz University of Technology (Author)
  • H. L. Yang - , Chemnitz University of Technology (Author)
  • J. Wang - , Chemnitz University of Technology (Author)
  • J. F. Fu - , Chemnitz University of Technology (Author)


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.


Original languageEnglish
Pages (from-to)111-119
Number of pages9
JournalThe European physical journal. B, Condensed matter and complex systems
Issue number1
Publication statusPublished - Sept 2009
Externally publishedYes



  • 02.30.Ks Delay and functional equations, 05.40.-a Fluctuation phenomena, random processes, noise, and Brownian motion, 05.45.-a Nonlinear dynamics and chaos