Reinhart Koselleck-Project

Projektseite auf Deutsch

Project description

The collective nonlinear dynamics and reliable function of complex networked systems fundamentally underlie our daily lives, whether in biological cells, in power grids or in ecosystems. Most complex systems from the natural and engineering sciences are externally driven, strongly affecting their dynamics. For instance, they may exhibit nonlinear state shifts or undergo tipping that disrupt the systems’ intended or desired functionality. While state-of-the-art theoretical concepts and method development have focused on linear responses suitable for weak driving signals, it is far less understood how to characterize, predict, and design complex systems responding to strong perturbations that, for example, may ultimately lead to tipping. The proposed project aims to newly invent and develop mathematical theoretical concepts, methods, and tools that are capable of helping to understand and quantify collective dynamics of strongly driven nonlinear and networked systems. The research will focus on strongly and continuously perturbed systems, as well as their generically nonlinear response and tipping properties. Specifically, we aim to learn how to theoretically predict genuinely nonlinear responses, develop tools to predict tipping dynamics caused by strong perturbations, understand how strong-signal responses distribute across networks, and design complex dynamical systems to be resilient or adapting to large perturbation signals. While the core work focuses on analytical and computational method development, we strive to test and apply our results in various realms, for instance in physics, biology, engineering as well as general dynamical systems modeling of applied mathematics.

Project data