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首页> 外文期刊>Proceedings of the Royal Society. Mathematical, physical and engineering sciences >Signatures of chaotic and stochastic dynamics uncovered with epsilon-recurrence networks
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Signatures of chaotic and stochastic dynamics uncovered with epsilon-recurrence networks

机译：epsilon递归网络揭示了混沌和随机动力学的特征

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摘要

An old and important problem in the field of nonlinear time-series analysis entails the distinction between chaotic and stochastic dynamics. Recently, e-recurrence networks have been proposed as a tool to analyse the structural properties of a time series. In this paper, we propose the applicability of local and global e-recurrence network measures to distinguish between chaotic and stochastic dynamics using paradigmatic model systems such as the Lorenz system, and the chaotic and hyper-chaotic Rossler system. We also demonstrate the effect of increasing levels of noise on these network measures and provide a real-world application of analysing electroencephalographic data comprising epileptic seizures. Our results show that both local and global e-recurrence network measures are sensitive to the presence of unstable periodic orbits and other structural features associated with chaotic dynamics that are otherwise absent in stochastic dynamics. These network measures are still robust at high noise levels and short data lengths. Furthermore, e-recurrence network analysis of the real-world epileptic data revealed the capability of these network measures in capturing dynamical transitions using short window sizes. e-recurrence network analysis is a powerful method in uncovering the signatures of chaotic and stochastic dynamics based on the geometrical properties of time series.
机译：非线性时间序列分析领域的一个古老而重要的问题是需要区分混沌动力学和随机动力学。最近，电子递归网络已被提出作为分析时间序列的结构特性的工具。在本文中，我们提出使用范式模型系统（例如Lorenz系统，混沌和超混沌Rossler系统）区分局部和全局电子递归网络度量以区分混沌和随机动力学的适用性。我们还展示了这些网络措施对噪声水平的影响，并为分析包括癫痫发作的脑电图数据提供了实际应用。我们的结果表明，本地和全局电子递归网络测度均对不稳定周期轨道的存在和与混沌动力学相关的其他结构特征敏感，否则在随机动力学中就不会出现这种现象。这些网络措施在高噪声水平和短数据长度下仍然很健壮。此外，对真实世界的癫痫数据的电子递归网络分析表明，这些网络措施具有使用短窗口大小捕获动态过渡的能力。电子递归网络分析是一种基于时间序列的几何特性来揭示混沌和随机动力学特征的有效方法。

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