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Published on: October 1, 2019
A criterion for safe overshoot in coupled tipping systems
S Sinet1, N A M Delmeire2, P D L Ritchie3
1Department of Physics, Institute for Marine and Atmospheric Research Utrecht, and Centre for Complex Systems Studies, Utrecht University, Utrecht, The Netherlands.
Chaos (Woodbury, N.Y.)
|July 30, 2026
Summary
Safe overshoots of critical thresholds, known as tipping points, can occur in interacting climate systems. New research derives a criterion for these safe overshoots in coupled slow-fast systems, considering timescale separation and coupling strength.
Area of Science:
- Climate science
- Ecological dynamics
- Complex systems analysis
Background:
- Abrupt transitions in climate and ecological systems are often linked to critical thresholds called tipping points.
- Previous studies established that finite-time overshoots of tipping points can be safe under specific conditions in isolated systems.
- The behavior of safe overshoots in interacting subsystems, however, remains less understood.
Purpose of the Study:
- To investigate safe-overshoot phenomena in unidirectionally coupled slow-fast systems.
- To derive a criterion for safe overshoots in interactive settings, analogous to the inverse-square law for isolated systems.
- To explore the influence of nonlinear interactions and time-derivative coupling on safe overshoots.
Main Methods:
- Development of theoretical criteria for safe overshoots in coupled systems.
- Analysis of slow-fast dynamical systems with nonlinear interactions.
- Application of the derived criterion to conceptual models involving the Atlantic Meridional Overturning Circulation, Amazon rainforest, and Greenland Ice Sheet.
Main Results:
- A novel criterion for safe overshoots in interactive slow-fast systems was derived.
- The criterion explicitly incorporates timescale separation and coupling strength between subsystems.
- The study demonstrates safe-overshoot phenomena in models of coupled climate-ecological systems.
Conclusions:
- Safe overshoots are possible in interacting systems, not just isolated ones.
- The derived criterion provides a framework for understanding safe transitions in complex, coupled environmental systems.
- This research contributes to predicting the stability and resilience of interconnected climate subsystems.
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