Nonlinear time series analysis of dynamical systems: Complexity quantification and correlation analysis

This thesis investigates the complexity of dynamical systems using a broad set of measures, including structural, entropic, dynamical, and recurrence-based approaches. These were systematically applied to low-dimensional, mostly deterministic systems, both continuous and discrete in time. Analyses were based on the full multidimensional output of each system, avoiding re-embedding from single components. While most measures performed reliably on long, unperturbed trajectories, some showed poor convergence. To assess redundancy and complementarity, statistical relationships between measures were examined. Strong correlations emerged, including between robust and more elusive measures, suggesting partial overlap and the potential for indirect inference.

This bachelor's thesis was submitted to the Institute of Physics at Humboldt-Universität zu Berlin on 4 July 2025. The work was carried out at the Potsdam Institute for Climate Impact Research (PIK), Research Department 4 – Complexity Science.