Chaotic Diffusion in Delay Systems

• Applicant: Professor Dr. Martin Weigel, since 8/2024
• Subject Area: Statistical Physics, Nonlinear Dynamics, Complex Systems, Soft and Fluid Matter, Biological Physics
• Term: since 2020
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 438881351

Chaotic diffusion is a well-known deterministic phenomenon in nonlinear dynamical systems, where the state variable shows normal or anomalous diffusive motion. A thorough understanding of the mechanisms leading to normal or anomalous diffusion was achieved mainly for low-dimensional dynamical systems. Recently renewed interest was triggered by questions of ergodicity breaking in such systems. Delay systems, on the other hand, are very general and practically relevant systems, where finite transmission times of reactions are explicitly taken into account. These formally infinite-dimensional systems have a long history, but surprisingly, the appearance of diffusive motion in such systems has hardly been investigated. Our recent detection of laminar chaos, a new form of chaotic motion in delay systems, provides also hitherto unknown mechanisms for normal and anomalous diffusion in delay systems, thus connecting two traditional branches of nonlinear dynamics. The general goal of this project is to explore the properties of diffusive motion in such delay systems, including questions of ergodicity breaking, and the scenarios appearing in the transition from laminar to turbulent chaos.

• DFG Programme: Research Grants
• Ehemaliger Antragsteller: Professor Dr. Günter Radons, until 7/2024 (†)