Regensburg 2019 – wissenschaftliches Programm

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DY: Fachverband Dynamik und Statistische Physik

DY 31: Nonlinear Dynamics, Synchronization and Chaos

DY 31.6: Vortrag

Mittwoch, 3. April 2019, 11:15–11:30, H20

Resonant Doppler effect from delayed feedback leads to multistability and generalized laminar chaos — •Andreas Otto, David Müller, and Günter Radons — Institute of Physics, Chemnitz University of Technology, 09107 Chemnitz, Germany

Delayed feedback or aftereffects can be found in many dynamical systems ranging, for example, from population dynamics to metal cutting. We show that the effect of a delay variation in such time delay systems is similar to the Doppler effect with self-feedback. We distinguish between the non-resonant and the resonant Doppler effect corresponding to the known dichotomy between conservative and dissipative delays [1]. The non-resonant Doppler effect leads to a quasiperiodic frequency modulation of the signal but the qualitative properties of the solution are the same as for constant delay systems.

In contrast, for the resonant Doppler effect the solutions are characterized by alternating low and high frequency phases. For large delays these phases are clearly separated, which is equivalent to time-multiplexed dynamics. This allows the design of well-defined multistable solutions or periodic temporal switching between different chaotic and periodic dynamics. We systematically study such kind of dynamics and present the most interesting examples. Finally, we show that the recently found laminar chaos [2] is only the zeroth-order case of a bigger class of chaos, which we call generalized laminar chaos.

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

[2] Müller, Otto, and Radons, Phys. Rev. Lett. 120, 084102 (2018).