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 [Hart, Roy, Müller-Bender, Otto, and Radons, Phys. Rev. Lett. 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.

中文翻译：

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实验中的层流混沌和非线性延迟Langevin方程：用于检测层流混沌的时间序列分析工具箱

最近，已经显示出某些时变延迟较大的系统表现出不同类型的混沌，这与两种时变延迟有关：保守延迟和耗散延迟。已知的高维湍流的特点是强烈的波动。相比之下，最近发现的低维层流混沌的特征是层流相位几乎恒定，具有周期性的持续时间，并且相位之间强度的混沌变化。在本文中，我们扩展了先前出版物中的结果[Hart，Roy，Müller-Bender，Otto和Radons，Phys。牧师 123，154101（2019）]，其中证明了层流混沌是一种鲁棒的现象，可以在实验系统中观察到。我们提供了一个时间序列分析工具箱，用于检测层流混沌的鲁棒性。我们通过模型系统的实验时间序列和时间序列对工具箱进行基准测试，该模型系统由具有时变延迟的非线性Langevin方程描述。对于实验系统和模型系统，都针对不同的噪声强度进行了基准测试，即使很难通过轨迹的视觉分析将其与湍流混沌区分开，也可以检测到层流混沌。