I. Introduction to the mathematics of change
- Modelling (nonlinear) growth and Deterministic Chaos (C1)
- Multivariate systems: Predator-Prey dynamics (C2)
- Potential theory, Agent-based models, Dynamic field models (C2)
II. Time Series Analysis: Temporal Correlations and Fractal Scaling
- Nonlinear regression: Fitting analytic solutions and Catastrophe Theory (C3)
- Basic timeseries analysis: Quantifying temporal correlations and order transitions (C4)
- Scaling phenomena: Fluctuation analyses and (multi-)fractal geometry (C5)
III. Quantifying Recurrences in State Space
- Takens’ Theorem and State-Space reconstruction (C6)
- Recurrence Quantification Analysis of continuous and categorical data (C6)
- Cross-Recurrence Quantification Analysis of dyadic interaction (C7)
- Early Warning Signals of order transitions (C7)
IV. Complex Networks
- Small-world and Scale-free networks (C8)
- Symptom networks and Networks of Quantified Recurrences (C8)
- Early Warning Signals of order transitions in clinical settings (C8)