Strongly Driven Nonlinear Network Dynamics

• Applicant: Professor Dr. Marc Timme, Ph.D.
• Subject Area: Statistical Physics, Nonlinear Dynamics, Complex Systems, Soft and Fluid Matter, Biological Physics
• Term: since 2024
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 544800752

The collective nonlinear dynamics and reliable function of complex 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 unexpected state shifts or undergo tipping that may 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 e.g., may ultimately lead to tipping. The proposed research 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 continuously perturbed systems and their genuinely 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, to understand how strong-signal responses distribute across networks and to 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 the realms of physics, biology, engineering as well as general dynamical systems modeling in applied mathematics.

• DFG Programme: Reinhart Koselleck Projects
• Cooperation Partner: Professorin Dr. Mor Nitzan
• Co-Investigator: Professor Dr. Benjamin Schäfer