Preprints
https://doi.org/10.5194/npg-2023-7
https://doi.org/10.5194/npg-2023-7
28 Mar 2023
 | 28 Mar 2023
Status: this preprint is currently under review for the journal NPG.

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

Ulrike Feudel

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.

Ulrike Feudel

Status: final response (author comments only)

Comment types: AC – author | RC – referee | CC – community | EC – editor | CEC – chief editor | : Report abuse
  • RC1: 'Comment on npg-2023-7', Anonymous Referee #1, 11 Apr 2023
  • RC2: 'Comment on npg-2023-7', Anonymous Referee #2, 29 Apr 2023

Ulrike Feudel

Ulrike Feudel

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Short summary
Many systems in nature are characterized by the coexistence of different stable states for given environmental parameters and external forcing. Examples can be found in different fields of science ranging from ecosystems to climate dynamics. Perturbations can lead to critical transitions (tipping) from one stable state to another. The study of these transitions requires the development of new methodological approaches that allow for modeling, analyzing, and predicting them.