Introduces the basic concepts of nonlinear dynamics and chaos and how they can be applied for the study of complex systems, spatiotemporal data, and nonlinear interrelationships in geosciences. Methods based on information theory, recurrences properties, and complex networks are taught and their potentials are demonstrated. The fundamentals of statistical tests are introduced and how to construct appropriate statistical tests for specific applications are discussed.
The specific topics contain
- Basic terminology, dynamical systems, and simple prototypical models
- Dimensions, fractals
- Concept of symbolic dynamics
- Concept of phase space, phase space reconstruction, Lyapunov exponent and correlation sum
- Concept of recurrence in phase space, recurrence plots, recurrence quantification analysis
- Detection of regime transitions, statistical tests
- Concept of synchronization, coupling analysis
- Spatial and spatio-temporal data analysis using recurrence features
- Complex networks, network models, measures, network representations
- Functional networks, reconstruction of networks, climate networks
- Complex networks based time series analysis
- Kursleiter:in: Tobias Braun
- Kursleiter:in: Kai Hauke Krämer
- Kursleiter:in: Norbert Marwan