Tipping resonance in a chaotically forced ice age model

TL;DR

This paper investigates how chaotic forcing influences rate-induced tipping in a low-order ice age model, revealing a resonance effect where certain forcing timescales maximize the likelihood of tipping between attractors.

Contribution

It demonstrates the existence of a resonance-like phenomenon in chaotic forcing-induced tipping, combining basin instability, Lyapunov exponents, and resonance analysis.

Findings

Chaotic forcing can trigger rate-induced tipping between attractors.

A resonance effect exists where certain timescales maximize tipping likelihood.

Theoretical analysis explains the resonance through basin instability and Lyapunov exponents.

Abstract

Many physical systems are forced by external inputs, which can sometimes take the form of chaotic variation. A particular example is found in applications related to weather and climate, where chaotic variation is prevalent across various timescales. If the system in question has multiple attracting solutions for a given range of forcing, rate-induced tipping can be triggered by the chaotic forcing, with the difference in timescales between the forcing and the system acting as a `rate' parameter. In this paper, we explore the interplay between these two timescales in a low-order model of ice age dynamics. The model exhibits bistability between two equilibria in one region of the parameter space and between an equilibrium and a periodic orbit in another region. When chaotic variation of the parameters is allowed within these bistable regions, the solutions of the forced system undergo rate-induced tipping from one attractor to another. Simulations of the forced system show that the timescale of the chaotic forcing induces a resonance-like behaviour, with an optimal timescale at which the likelihood of rate-induced tipping is at its maximum. We combine basin instability theory, finite-time Lyapunov exponents, and linear resonance analysis under periodic forcing to explain this resonance effect.