Tipping resonance in a chaotically forced ice age model
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866918390481813504 |
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| author | Quinn, Courtney Alkhayuon, Hassan |
| author_facet | Quinn, Courtney Alkhayuon, Hassan |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_15043 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Tipping resonance in a chaotically forced ice age model Quinn, Courtney Alkhayuon, Hassan Chaotic Dynamics Dynamical Systems 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. |
| title | Tipping resonance in a chaotically forced ice age model |
| topic | Chaotic Dynamics Dynamical Systems |
| url | https://arxiv.org/abs/2603.15043 |