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SOE: Fachverband Physik sozio-ökonomischer Systeme
SOE 17: Networks: From Topology to Dynamics (joint session SOE/DY)
SOE 17.7: Talk
Wednesday, March 20, 2024, 16:45–17:00, TC 006
Nonequilibrium Nonlinear Dynamics I: Nonlinear Shift and Tipping — Julian Fleck1, Moritz Thümler1, Malte Schröder1, Seungjae Lee1, and •Marc Timme1,2 — 1Center for Advancing Electronics Dresden (cfaed) and Institute for Theoretical Physics, Technische Universität Dresden, 01062 Dresden, Germany — 2Lakeside Labs, 9020 Klagenfurt am Wörthersee, Austria
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, and may exhibit intrinsically 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 e.g., may ultimately lead to tipping. Here we report average response offsets that scale nonlinearly at asymptotically small amplitudes. At some critical driving amplitude, responses cease to stay close to a given operating point and may diverge. Standard response theory fails to predict these amplitudes even at arbitrarily high orders. We propose an integral self-consistency condition that captures the full nonlinear response dynamics. We illustrate our approach for a minimal one-dimensional model and capture the nonlinear shift of voltages in the response dynamics of AC power grid networks.
Keywords: network dynamics; nonlinear dynamics; response theory; non-autonomous dynamics; coupled oscillators