Tipping resonance in a chaotically forced ice age model
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Date
2026-03-16
Authors
Quinn, Courtney
Alkhayuon, Hassan
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Publisher
arXiv
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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.
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Keywords
nlin.CD , math.DS , [Maths] , Chaotic variation
Citation
Quinn, C & Alkhayuon, H 2026 'Tipping resonance in a chaotically forced ice age model' arXiv, pp. 1-21.
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© 2026, the Authors.