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Experimental Methods to Study Human Postural Control

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Published on: September 11, 2019

Recovery-induced tipping in Stommel's kicked ocean box model.

Peter Kelly¹, Xinyi Leng¹, Pascal Cogan¹

¹Department of Mathematics and Statistics, Carleton College, Northfield, Minnesota, United States of America.

|February 3, 2026

Summary

Extended recovery periods between disturbances can unexpectedly shift ocean circulation models to new states. This research explores recovery-induced tipping in Stommel

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Area of Science:

Oceanography
Climate Science
Dynamical Systems Theory

Background:

Ocean circulation is a critical component of global climate regulation.
Thermohaline circulation is susceptible to disruptions, such as freshwater input from melting glaciers.
Stommel's two-box model provides a framework for understanding ocean circulation dynamics and salinity perturbations.

Purpose of the Study:

To investigate the phenomenon of recovery-induced tipping in a perturbed Stommel ocean circulation model.
To analyze the robustness of this tipping phenomenon across various disturbance parameters and kick sizes.
To elucidate the underlying dynamical mechanisms driving the system's transition to an alternative attractor.

Main Methods:

Superimposing discrete salinity perturbations ('kicks') onto a continuous flow in Stommel's two-box model.
Analyzing the model's trajectory behavior as recovery periods between perturbations are extended.
Employing bifurcation analysis of flow-kick fixed points to understand attractor migration.

Main Results:

Extending the recovery time between salinity perturbations can lead to counterintuitive tipping into an alternative basin of attraction.
The recovery-induced tipping phenomenon is robust across a significant range of kick sizes.
Bifurcation analysis reveals tipping occurs due to an alternative attractor crossing a separatrix as flow times change.

Conclusions:

The study confirms the robustness of recovery-induced tipping in Stommel's perturbed model.
The underlying mechanism involves the migration of an alternative attractor.
While natural freshwater influx recovery times are longer, the discovered dynamics may be relevant to other complex systems.