Laminar Chaos in experiments and nonlinear delayed Langevin equations: A time series analysis toolbox for the detection of Laminar Chaos
arXiv:2003.00850 · doi:10.1103/PhysRevE.101.032213
Abstract
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 dissipative delays. The known high-dimensional Turbulent Chaos is characterized by strong fluctuations. In contrast, the recently discovered low-dimensional Laminar Chaos is characterized by nearly constant laminar phases with periodic durations and a chaotic variation of the intensity from phase to phase. In this paper we extend our results from our preceding publication [J. D. Hart, R. Roy, D. Müller-Bender, A. Otto, and G. Radons, PRL 123 154101 (2019)], where it is demonstrated that Laminar Chaos is a robust phenomenon, which can be observed in experimental systems. We provide a time-series analysis toolbox for the detection of robust features of Laminar Chaos. We benchmark our toolbox by experimental time series and time series of a model system which is described by a nonlinear Langevin equation with time-varying delay. The benchmark is done for different noise strengths for both the experimental system and the model system, where Laminar Chaos can be detected, even if it is hard to distinguish from Turbulent Chaos by a visual analysis of the trajectory.
arXiv comment16 pages, 14 figures; v2: minor corrections, typos; v3: minor corrections, typos, added journal reference and DOI
References in corpus (17)
- Tutorial: Photonic Neural Networks in Delay Systems
- Stochastic processes with distributed delays: chemical Langevin equation and linear-noise approximation
- Chaos in time delay systems, an educational review
- Stochastic thermodynamics of Langevin systems under time-delayed feedback control: I. Second-law-like inequalities
- A delay differential model of ENSO variability: Parametric instability and the distribution of extremes
- Amplitude death in oscillator networks with variable-delay coupling
- Leveraging Chaos for Wave-Based Analog Computation: Demonstration with Indoor Wireless Communication Signals
- Stabilization of unstable steady states by variable delay feedback control
- Laminar Chaos
- Experiments with arbitrary networks in time-multiplexed delay systems
- Variable-delay feedback control of unstable steady states in retarded time-delayed systems
- Chaos Synchronization of delayed systems in the presence of delay time modulation
- Characteristics of a Delayed System with Time-dependent Delay Time
- Delayed feedback control of unstable steady states with high-frequency modulation of the delay
- Synchronization of Chaotic Oscillators due to Common Delay Time Modulation
- From dynamical systems with time-varying delay to circle maps and Koopmanism
- The Mid-Pleistocene Transition induced by delayed feedback and bistability