Tipping points induced by parameter drift in an excitable ocean model

Numerous systems in the climate sciences and elsewhere are excitable, exhibiting coexistence of and transitions between a basic and an excited state. We examine the role of tipping between two such states in an excitable low-order ocean model. Ensemble simulations are used to obtain the model's pullback attractor (PBA) and its properties, as a function of a forcing parameter gamma and of the steepness delta of a climatological drift in the forcing. The tipping time ttp is defined as the time at which the transition to relaxation oscillations (ROs) arises: at constant forcing this occurs at gamma=gamma c. As the steepness delta decreases, ttp is delayed and the corresponding forcing amplitude decreases, while remaining always above gamma c. With periodic perturbations, that amplitude depends solely on delta over a significant range of parameters: this provides an example of rate-induced tipping in an excitable system. Nonlinear resonance occurs for periods comparable to the RO time scale. Coexisting PBAs and total independence from initial states are found for subsets of parameter space. In the broader context of climate dynamics, the parameter drift herein stands for the role of anthropogenic forcing.

Automated summary

This study explores the tipping between two states in an excitable low-order ocean model, discovering the relationship between tipping time and forcing amplitude. Rate-induced tipping in an excitable system is observed within a significant range of parameters, along with nonlinear resonance and coexisting attractors in parameter space.