2026/02/23 by Sacha Sinet, S. Sinet, Nathalie A. M. Delmeire +8 · 1 voice
Environmental Science · Physics and Astronomy · #Chaos control and synchronization #Control theory (sociology) #Coupling (piping) #Ecosystem dynamics and resilience #Nonlinear system #Overshoot (microwave communication) #Tipping point (physics) #Work (physics) #nlin.CD #stochastic dynamics and bifurcation
paper · pdf · doi:10.1063/5.0332433
arxiv published 2026/02/23 · arxiv updated 2026/02/23 · openalex publication_date 2026/07/01 · openalex created_date 2026/07/31 · openalex updated_date 2026/08/01
Abrupt transitions are a central concern in climate and ecological research and may arise when critical thresholds known as tipping points are crossed. However, previous work has shown that finite-time overshoots of tipping points can be safe, and that such behavior is captured by an inverse-square-law criterion when overshoots are sufficiently small and slow. So far studied in isolated systems with external drivers, (un)safe overshoots may also emerge from interactions between subsystems. Here, we investigate safe-overshoot phenomena in unidirectionally coupled slow-fast systems featuring both nonlinear interactions and coupling through time derivatives. Specifically, we derive a criterion for the occurrence of safe overshoots analogous to the inverse-square law for isolated systems, but adapted to interactive settings, and expressed explicitly in terms of the timescale separation and coupling strength between subsystems. We illustrate these results using two conceptual models in which the Atlantic Meridional Overturning Circulation interacts with either the Amazon rainforest or the Greenland Ice Sheet.