Recurrence plot analysis of regime changes in dynamical Systems

动态系统中的过渡，如临界点或政权转移，在生活，自然或技术世界的所有领域都是无处不在的。了解这种转变对于早期发现和控制这些转变非常重要。递归图框架为识别状态转换提供了多功能工具。拟议的项目系统地研究递归图的功能和相应的递归量化措施相对于动态系统的动态特性的变化。通过这种方式，它通过将某些类别的复发模式与典型的动态和转换联系起来，填补了复发分析中的空白。另一个目标是制定一个强大的显着性测试和方法，帮助应用递归分析不规则采样的时间序列以及数据的不确定性。这些新的事态发展将有助于更好地了解突然的过渡和政权更迭，并采用基于重现的过渡预警措施。复发的概念，然后将被应用于回答选定的研究问题，在神经科学，气候学和工程学的不同科学学科中，过渡发挥了重要作用：在颅内EEG测量中识别过渡到所谓的发作前状态和从所谓的发作前状态是定义癫痫发作的前兆的第一步。对东非古气候转变的分析将有助于了解新生代（最近的地质时代，涵盖过去6600万年）期间东非环境稳定与不稳定之间转换的可能机制。热声不稳定性的转变的表征和火焰熄灭的前体的定义有助于更可靠和更有效的燃烧过程的发展。在这些不同的应用程序中遇到的挑战和差异，将提供在不同的科学学科的递归为基础的过渡分析的指导方针。

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.