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Mathematics > Dynamical Systems

arXiv:2210.00873 (math)
[Submitted on 3 Oct 2022]

Title:Rate and Noise-Induced Tipping Working in Concert

Authors:Katherine Slyman, Christopher K. Jones
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Abstract:Rate-induced tipping occurs when a ramp parameter changes rapidly enough to cause the system to tip between co-existing, attracting states. We show that the addition of noise to the system can cause it to tip well below the critical rate at which rate-induced tipping would occur. Moreover it does so with significantly increased probability over the noise acting alone. We achieve this by finding a global minimizer in a canonical problem of the Freidlin-Wentzell action functional of large deviation theory that represents the most probable path for tipping. This is realized as a heteroclinic connection for the Euler-Lagrange system associated with the Freidlin-Wentzell action and we find it exists for all rates less than or equal to the critical rate. Its role as most probable path is corroborated by direct Monte Carlo simulations.
Subjects: Dynamical Systems (math.DS)
Cite as: arXiv:2210.00873 [math.DS]
  (or arXiv:2210.00873v1 [math.DS] for this version)
  https://doi.org/10.48550/arXiv.2210.00873
Related DOI: https://doi.org/10.1063/5.0129341

Submission history

From: Katherine Slyman [view email]
[v1] Mon, 3 Oct 2022 12:31:52 UTC (4,812 KB)
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