Rethinking the Definition of Rate-Induced Tipping

Abstract

The current definition of rate-induced tipping is tied to the idea of a pullback attractor limiting in forward and backward time to a stable quasi-static equilibrium. Here we propose a new definition that encompasses the standard definition in the literature for certain scalar systems and includes previously excluded $N$-dimensional systems that exhibit rate-dependent critical transitions.

11 pages, 5 figures

References in corpus (1)

• Rate-induced tipping and saddle-node bifurcation for a class of quadratic differential equations with nonautonomous asymptotic dynamics

Cited by in corpus (2)

• Attractors and bifurcation diagrams in complex climate models
• Tipping detection using climate networks