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DY: Fachverband Dynamik und Statistische Physik

DY 8: Focus Session: Nonlinear Dynamics and Stochastic Processes – Advances in Theory and Applications II

DY 8.10: Talk

Monday, March 17, 2025, 18:00–18:15, H43

Chaotic Diffusion in Systems with Delay — •Tony Albers, David Müller-Bender, and Lukas Hille — Institute of Physics, Chemnitz University of Technology, Chemnitz, Germany

Chaotic Diffusion is a purely deterministic phenomenon occurring in nonlinear systems. While much is known about chaotic diffusion in low-dimensional dynamical systems such as iterated maps or Hamiltonian systems, there are only a few works dealing with chaotic diffusion in higher-dimensional systems. In this talk, we show that chaotic diffusion is also possible in dynamical systems with time delay, which raises the dimension of the problem formally to infinity. Moreover, we demonstrate that introducing a periodic modulation of the delay can increase the strength of the diffusion, as measured by the diffusion coefficient, by several orders of magnitude [1]. This phenomenon is counterintuitively related to a significant decrease of the Kaplan-Yorke dimension of the chaotic attractor due to the appearance of so-called laminar chaos [2], which is a recently discovered type of chaos that is not observed in systems with constant delay. We acknowledge the contributions of the late Günter Radons who initiated this work.

[1] Tony Albers, David Müller-Bender, Lukas Hille, and Günter Radons, Phys. Rev. Lett. 128, 074101 (2022)

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

Keywords: Chaotic Diffusion; Delay Systems; Laminar Chaos