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DY: Fachverband Dynamik und Statistische Physik

DY 42: Delay and Feedback Dynamics

DY 42.4: Talk

Thursday, March 19, 2015, 10:30–10:45, BH-N 128

A fundamental dichotomy for dynamical systems with variable delay — •Andreas Otto, David Müller, and Günter Radons — Institute of Physics, Chemnitz University of Technology, 09107 Chemnitz, Germany

Dynamical systems with time-varying delays can describe various phenomena in many fields such as biology, chemistry, economy, engineering and physics. We identify two fundamentally different classes of variable delays. Conservative delays are related to quasiperiodicity and are equivalent to constant delays. On the other hand, contractive delays are characterized by mode-locking and cannot be converted to constant delays.

Time-varying delays are often generated by a common transport mechanism resulting in a conservative delay. However, typical models for time-varying delays often represent both, conservative and contractive delays, depending extremely sensitive on the delay parameters. In fact, starting from a conservative delay, we show that no continuous parameter change is possible without passing a contractive delay or equivalently modeling unphysical situations.

The type of the delay affects the dynamics of the associated time delay system. For conservative delays the asymptotic scaling of the Lyapunov spectrum is logarithmic, similar to the well-known behavior for constant delays. In contrast, for contractive delays the asymptotic scaling of the Lyapunov spectrum is linear. The presented results are independent of the specific form or the attractor of the time delay system as well as independent of the specific form of the variable delay.