Berlin 2018 – scientific programme

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DY: Fachverband Dynamik und Statistische Physik

DY 33: Delay and Feedback Dynamics

DY 33.3: Talk

Tuesday, March 13, 2018, 14:30–14:45, BH-N 334

Small changes, big effect: The dimension of chaotic attractors of dynamical systems with time-varying delay — •David Müller, Andreas Otto, and Günter Radons — Institute of Physics, Chemnitz University of Technology, 09107 Chemnitz, Germany

For many systems arising in biology, climate dynamics and engineering the influence of time-delays can not be neglected. Although taking into account environmental fluctuations by introducing time-varying delays can lead to more realistic models, the delay is often considered constant and only a few publications deal with the effect of a time-varying delay on the dynamics of the involved systems.

Recently, we identified two classes of time-varying delays, which are characterized by fundamental differences in the tangent space dynamics of the related systems [1,2]. In this talk, we demonstrate that introducing a time-varying delay also leads to drastic differences in the properties of chaotic attractors of systems with large delay. In detail, the dimension of chaotic attractors of systems with conservative delay is typically much larger than the dimension of attractors of systems with dissipative delay. Due to the fractal dependence of the delay class on the delay parameters, arbitrary small changes of the delay parameters can cause huge variations of the attractor dimension.

[1] A. Otto, D. Müller and G. Radons, Phys. Rev. Lett. 118, 044104 (2017).

[2] D. Müller, A. Otto and G. Radons, Phys. Rev. E 95, 062214 (2017).