The effect of timescale separation on the tipping window for chaotically forced systems Article Swipe

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YOU? · · 2025 · Open Access · · DOI: https://doi.org/10.48550/arxiv.2504.12530

Tipping behaviour can occur when an equilibrium loses stability in response to a slowly varying parameter crossing a bifurcation threshold, or where noise drives a system from one attractor to another, or some combination of these effects. Similar behaviour can be expected when a multistable system is forced by a chaotic deterministic system rather than by noise. In this context, the chaotic tipping window was recently introduced and investigated for discrete-time dynamics. In this paper, we find tipping windows for continuous-time nonlinear systems forced by chaos. We characterise the tipping window in terms of forcing by unstable periodic orbits of the chaos, and we show how the location and structure of this window depend on the relative timescales between the forcing and the responding system. We illustrate this by finding tipping windows for two examples of coupled bistable ODEs forced with chaos. Additionally, we describe the dynamic tipping window in the setting of a changing system parameter.

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Type: preprint
Language: en
Landing Page: http://arxiv.org/abs/2504.12530
PDF: https://arxiv.org/pdf/2504.12530
OA Status: green
OpenAlex ID: https://openalex.org/W4417089462

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DOI: https://doi.org/10.48550/arxiv.2504.12530

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Title: The effect of timescale separation on the tipping window for chaotically forced systems

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Type: preprint

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Language: en

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Publication year: 2025

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Publication date: 2025-04-16

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Authors: Raphael Römer, Peter Ashwin

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Landing page: https://arxiv.org/abs/2504.12530

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PDF URL: https://arxiv.org/pdf/2504.12530

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OA status: green

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Cited by: 0

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