Recurrence plot analysis of regime changes in dynamical Systems

动力系统的转变，如临界点或制度转变，在生活、自然或技术世界的所有领域无处不在。对这种转变的理解对于及早发现和控制它们是很重要的。重现图框架为识别政权过渡提供了多才多艺的工具。该项目系统地研究了递归图中的特征以及与动力系统动力学特征变化相关的相应的递归量化措施。通过这种方式，它通过将某些类型的重现模式与典型的动态和转换相关联，填补了重现分析中的空白。另一个目标是开发一种稳健的显著性检验和方法，帮助将递归分析应用于不规则抽样的时间序列以及具有不确定性的数据。这些新的事态发展将有助于更好地了解突然过渡和政权更迭，并引入基于复发的过渡预警措施。然后，复发的概念将被应用于回答神经科学、气候学和工程学等不同科学学科中的选定研究问题，其中过渡起着重要的作用：在颅内EEG测量中识别从癫痫发作前状态到癫痫发作前状态的转变是确定癫痫发作前兆的第一步。对东非古气候转变的分析将有助于揭示在新生代(最近的地质时代，涵盖过去6600万年)东非环境稳定和不稳定之间转换的可能机制。向热声不稳定性转变的特征和火焰熄灭前驱物的定义有助于发展更可靠和更有效的燃烧过程。在这些不同的应用中遇到的挑战和差异将为不同科学学科中基于递归的过渡分析提供指导。

Transitions in dynamical systems such as tipping points or regime shifts are ubiquitous in all areas of life, nature, or in the technical world. The understanding of such transitions is important for their early detection and their control. The recurrence plot framework provides versatile tools for the identification of regime transitions. The proposed project investigates systematically the features in recurrence plots and the corresponding recurrence quantification measures with respect to characteristic changes in the dynamics of dynamical systems. In this way, it fills a gap in recurrence analysis by linking certain classes of recurrence patterns to typical dynamics and transitions. A further goal is the development of a robust significance test and of approaches that help to apply recurrence analysis to irregularly sampled time series as well as to data with uncertainties. These new developments will help to better understand abrupt transitions and regime changes and to introduce recurrence based measures for early warning of transitions. The recurrence concept will then be applied to answer selected research questions in the different scientific disciplines of neuroscience, climatology, and engineering where transitions play an important role: The identification of transitions to and from so-called preictal states within intracranial EEG measurements is the first step in defining precursors of epileptic seizures. The analysis of the palaeo-climate transitions in East Africa will shade light on the possible mechanisms responsible for the switching between environmental stability and instability in Eastern Africa during the Cenozoic (the most recent geological era, covering the last 66 million years). The characterisation of the transitions to thermoacoustic instability and the definition of precursors for flame blowout contributes to the development of more reliable and efficient combustion processes. The challenges and differences met in these different applications will provide guidelines for recurrence based transition analysis in different scientific disciplines.