Rate-induced tipping in ecosystems and climate: the role of unstable states, basin boundaries and transient dynamics

Abstract

Abstract. The climate system as well as ecosystems might undergo relatively sudden qualitative changes in the dynamics when environmental parameters or external forcings vary due to anthropogenic influences. The study of these qualitative changes, called tipping phenomena, requires the development of new methodological approaches that allow modeling, analyzing, and predicting observed phenomena in nature, especially concerning the climate crisis and its consequences. Here we briefly review the mechanisms of classical tipping phenomena and investigate in more detail rate-dependent tipping phenomena which occur in non-autonomous systems characterized by multiple timescales. We focus on the mechanism of rate-induced tipping caused by basin boundary crossings. We unravel the mechanism of this transition and analyze, in particular, the role of such basin boundary crossings in non-autonomous systems when a parameter drift induces a saddle-node bifurcation in which new attractors and saddle points emerge, including their basins of attraction. Furthermore, we study the detectability of those bifurcations by monitoring single trajectories in state space and find that depending on the rate of environmental parameter drift, such saddle-node bifurcations might be masked or hidden and they can be detected only if a critical rate of environmental drift is crossed. This analysis reveals that quasi-stationary saddle points in non-autonomous multistable systems are the organizing centers of the global dynamics and need much more attention in future studies.

Alternative climatic steady states for the Permian-Triassic paleogeography

“…Also shock-induced tipping (S-tipping) can be caused by volcanic activity, or alternatively by asteroid impacts (O' Keefe and Ahrens, 1989), or any other mechanisms inducing a shift to another attractor on a shorter time scale than N-tipping. Finally, a forcing that varies on a time scale faster than the attractor internal variability can give rise to rate-induced tipping (R-tipping), even in the absence of multistability (Ashwin et al, 2017;Hoyer-Leitzel and Nadeau, 2021;Feudel, 2023;Ritchie et al, 2023).…”

Steady states and bifurcation diagram for the Permian-Triassic paleogeography

“…Also shock-induced tipping (S-tipping) can be caused by volcanic activity, or alternatively by asteroid impacts (O'Keefe and Ahrens 1989), or any other mechanism inducing a shift to another attractor on a shorter time scale than N-tipping. Finally, forcing that varies on a time scale faster than the attractor internal variability can give rise to rate-induced tipping (R-tipping), even in the absence of multistability (Ashwin et al 2017;Hoyer-Leitzel and Nadeau 2021;Feudel 2023;Ritchie et al 2023).…”