Recurrence plot analysis of regime changes in dynamical Systems

• Applicant: Privatdozent Dr. Norbert Marwan
• Subject Area: Statistical Physics, Nonlinear Dynamics, Complex Systems, Soft and Fluid Matter, Biological Physics
• Term: from 2017 to 2021
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 386137731

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.

• DFG Programme: Research Grants
• Co-Investigator: Professor Dr. Martin Trauth
• Cooperation Partner: Dr. Nadine Berner