Recurrence plot analysis of regime changes in dynamical Systems

在生活、自然或技术世界的所有领域，诸如临界点或政权转移之类的动态系统中的过渡无处不在。了解这种转变对其早期发现和控制非常重要。递归图框架为识别状态转换提供了多种工具。提出的项目系统地研究了递归图的特征和相应的递归量化措施，这些措施与动力系统动力学的特征变化有关。通过这种方式，它通过将某些类型的递归模式与典型的动态和转换联系起来，填补了递归分析中的空白。进一步的目标是开发一种鲁棒性显著性检验和有助于将递归分析应用于不规则采样时间序列以及具有不确定性的数据的方法。这些新的发展将有助于更好地了解突变和制度变化，并引入基于复发的措施来预警突变。然后，递归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选择的研究问题，在这些学科中，转换起着重要的作用：在颅内脑电图测量中识别所谓的前驱状态的转换是定义癫痫发作前驱的第一步。对东非古气候变化的分析将有助于揭示东非在新生代（最近的地质时代，覆盖过去6600万年）期间环境稳定与不稳定之间转换的可能机制。向热声不稳定过渡的特征和火焰喷灭前体的定义有助于开发更可靠和有效的燃烧过程。在这些不同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转移分析提供指导。

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.