Cascading Transitions in the Weak and Strong Coupling Limit

Many components of the Earth system are thought to be prone to dangerous transitions, presenting a big challenge for human societies. Known as tipping elements, those form an intricate network of interacting subsystems, creating the possibility of cascading critical transitions. The presence of those interacting tipping events makes it hard to predict the outcome of climate change. In this research, we investigate those phenomena above the usual approach of linearly interacting bistable components.

We propose to study generic nonlinear systems under generic nonlinear interaction. As a first step, we focus on unilaterally coupled components, where a leading and a following subsystem are naturally identified. Using singular perturbation methods, we show how the stability landscape can be approached semi-analytically when considering the weak and strong coupling limit. With only limited knowledge about the system's structure, this method applies to a wide class of interacting systems and allows for approaching steady states with a controlled error. This provides information on important structural features of the bifurcation diagram such as the presence of steady branches, their stability, and bifurcations. Finally, we illustrate our results using climate relevant conceptual models.