Time-series-analysis-based detailing of critical transitions in non-autonomous dynamical systems

• Applicant: Professor Dr. Klaus Lehnertz
• Subject Area: Statistical Physics, Nonlinear Dynamics, Complex Systems, Soft and Fluid Matter, Biological Physics
• Term: since 2025
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 555510056

Natural non-autonomous systems are far-from-equilibrium systems that evolve in and are driven by time-varying environments. These systems can exhibit dynamics with multiple time scales, transient behavior but also critical transitions to very different and sometimes even catastrophic dynamical regimes. Examples include epileptic seizures, extreme weather events, and large-scale failures in power supply networks. Since critical transitions have a massive impact on system functionality, it is crucial to better understand the underlying mechanisms, identify precursors of such transitions and reliably detect them in time series of suitable system observables in order to make forecasts and, if necessary, develop avoidance/mitigation strategies. Despite various mathematical models for critical transitions, a general understanding of the mechanisms underlying the occurrence of critical transitions in natural, non-autonomous systems is still lacking. There is, however, a wealth of observational data suitable for time-series-analysis-based detection and detailing of transitions in real-world systems. With our research program, we aim to develop -- in conjunction with the various proposed mathematical transition models -- time-series-analysis methods that are general enough to allow robust identification, differentiation, and adequate characterization of critical transitions. Two conceptually simple but widely applicable analysis techniques from the fields of symbolic dynamics and complex networks will serve as a basis. In preliminary studies, these have already proven to be promising for the issues to be addressed in the course of this project. By means of application-oriented method developments and computer simulations as well as through analyses of the dynamics of real-world systems, we aim to achieve an improved understanding of the emergence of critical transitions and to reliably identify precursors of such transitions.

• DFG Programme: Research Grants