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DY: Fachverband Dynamik und Statistische Physik

DY 12: Nonlinear Dynamics, Synchronization and Chaos I

DY 12.6: Vortrag

Dienstag, 12. März 2013, 10:45–11:00, H48

The relevance of Arnold tongues for systems with time-varying delay — •Andreas Otto, David Müller, and Günter Radons — Institute of Physics, Chemnitz University of Technology, 09107 Chemnitz, Germany

Is it possible to convert a dynamical system with variable time delay into a system with constant delay? In this talk nonlinear time scale transformations of time delay systems are investigated, which are connected with a topological conjugation of the retarded arguments of the delay differential equations.

A necessary and sufficient condition for the existence and a method for the transformation of systems with time-varying delay to systems with constant delay are presented. For instance, in case of a time-varying delay similar to a circle map the existence of a transformation to constant delay depends on whether the parameters of the variable delay are located in an Arnold tongue or not.

The results can be helpful for the numerical solution and the characterization of the dynamical behavior of non-autonomous delay differential equations.