Rethinking the Definition of Rate-Induced Tipping

TL;DR

This paper proposes a new, more inclusive definition of rate-induced tipping that applies to both scalar and higher-dimensional systems, expanding the understanding of rate-dependent critical transitions.

Contribution

It introduces a generalized definition of rate-induced tipping that covers systems previously excluded by standard definitions, including N-dimensional systems.

Findings

The new definition encompasses scalar systems with existing criteria.

It extends to N-dimensional systems exhibiting rate-dependent transitions.

Provides a unified framework for understanding 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.