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Complex behavior of simple maps with fluctuating delay times.
- Source :
-
European Physical Journal B: Condensed Matter . Sep2009, Vol. 71 Issue 1, p111-119. 9p. 17 Graphs. - Publication Year :
- 2009
-
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. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 14346028
- Volume :
- 71
- Issue :
- 1
- Database :
- Academic Search Index
- Journal :
- European Physical Journal B: Condensed Matter
- Publication Type :
- Academic Journal
- Accession number :
- 44445210
- Full Text :
- https://doi.org/10.1140/epjb/e2009-00262-8