Regensburg 2016 – scientific programme

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DY: Fachverband Dynamik und Statistische Physik

DY 51: Delay and feedback Dynamics

DY 51.1: Talk

Thursday, March 10, 2016, 10:00–10:15, H47

Dynamical systems with time-varying delay: Dissipative and more dissipative systems — •David Müller, Andreas Otto, and Günter Radons — Institute of Physics, Chemnitz University of Technology, 09107 Chemnitz, Germany

Dynamical systems with time-varying delay arise in many fields such as biology, chemistry, economy, engineering and physics.

We identify two different classes of systems with time-varying delay, whereby the the classification depends only on the characteristics of the delay. Systems with conservative delay can be transformed to systems with constant delay. Consequently, they exhibit the same type of dynamics. Systems with dissipative delay can not be transformed to systems with constant delay and the related dynamics differs from the dynamics of systems with constant delay. In typical models the delay is given by a parameter family. The systems show both types of delays and in general the delay type depends in a fractal manner on the delay parameters.

The difference in the dynamics of the delay classes becomes clear by the analysis of the evolution of small volumes on finite-dimensional subspaces of the infinite-dimensional state space of the delay system. For constant and conservative delays the system is dissipative. Hence, conservative time-varying delays “conserve” the well-known scaling behavior of the mean relaxation rate of the volume evolution corresponding to constant delays, which leads to the known logarithmic scaling of the Lyapunov spectrum. Dissipative delays lead to an additional contribution to the relaxation rate and change the scaling behavior.