Chaos in time delay systems, an educational review
H Wernecke, B Sándor, C Gros - Physics Reports, 2019 - Elsevier
The time needed to exchange information in the physical world induces a delay term when
the respective system is modeled by differential equations. Time delays are hence …
the respective system is modeled by differential equations. Time delays are hence …
Learning Hamiltonian neural Koopman operator and simultaneously sustaining and discovering conservation laws
Accurately finding and predicting dynamics based on the observational data with noise
perturbations is of paramount significance but still a major challenge presently. Here, for the …
perturbations is of paramount significance but still a major challenge presently. Here, for the …
Chaotic diffusion in delay systems: Giant enhancement by time lag modulation
T Albers, D Müller-Bender, L Hille, G Radons - Physical Review Letters, 2022 - APS
We consider a typical class of systems with delayed nonlinearity, which we show to exhibit
chaotic diffusion. It is demonstrated that a periodic modulation of the time lag can lead to an …
chaotic diffusion. It is demonstrated that a periodic modulation of the time lag can lead to an …
Laminar chaos in systems with quasiperiodic delay
D Müller-Bender, G Radons - Physical Review E, 2023 - APS
A type of chaos called laminar chaos was found in singularly perturbed dynamical systems
with periodic time-varying delay [Phys. Rev. Lett. 120, 084102 (2018)] 0031-9007 …
with periodic time-varying delay [Phys. Rev. Lett. 120, 084102 (2018)] 0031-9007 …
Laminar chaos in experiments: Nonlinear systems with time-varying delays and noise
A new type of dynamics called laminar chaos was recently discovered through a theoretical
analysis of a scalar delay differential equation with time-varying delay. Laminar chaos is a …
analysis of a scalar delay differential equation with time-varying delay. Laminar chaos is a …
Laminar chaos in experiments and nonlinear delayed Langevin equations: A time series analysis toolbox for the detection of laminar chaos
Recently, it was shown that certain systems with large time-varying delay exhibit different
types of chaos, which are related to two types of time-varying delay: conservative and …
types of chaos, which are related to two types of time-varying delay: conservative and …
From dynamical systems with time-varying delay to circle maps and Koopman operators
In this paper, we investigate the influence of the retarded access by a time-varying delay on
the dynamics of delay systems. We show that there are two universality classes of delays …
the dynamics of delay systems. We show that there are two universality classes of delays …
Laminar chaos in nonlinear electronic circuits with delay clock modulation
We study laminar chaos in an electronic experiment. A two-diode nonlinear circuit with
delayed feedback shows chaotic dynamics similar to the Mackey-Glass or Ikeda delay …
delayed feedback shows chaotic dynamics similar to the Mackey-Glass or Ikeda delay …
Resonant Doppler effect in systems with variable delay
D Müller-Bender, A Otto… - … Transactions of the …, 2019 - royalsocietypublishing.org
We demonstrate that a time-varying delay in nonlinear systems leads to a rich variety of
dynamical behaviour, which cannot be observed in systems with constant delay. We show …
dynamical behaviour, which cannot be observed in systems with constant delay. We show …