Probability of noise- and rate-induced tipping

Paul Ritchie and Jan Sieber
Phys. Rev. E 95, 052209 – Published 12 May 2017

Abstract

We propose an approximation for the probability of tipping when the speed of parameter change and additive white noise interact to cause tipping. Our approximation is valid for small to moderate drift speeds and helps to estimate the probability of false positives and false negatives in early-warning indicators in the case of rate- and noise-induced tipping. We illustrate our approximation on a prototypical model for rate-induced tipping with additive noise using Monte Carlo simulations. The formula can be extended to close encounters of rate-induced tipping and is otherwise applicable to other forms of tipping. We also provide an asymptotic formula for the critical ramp speed of the parameter in the absence of noise for a general class of systems undergoing rate-induced tipping.

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  • Received 16 January 2017
  • Revised 12 April 2017

DOI:https://doi.org/10.1103/PhysRevE.95.052209

©2017 American Physical Society

Physics Subject Headings (PhySH)

Nonlinear DynamicsStatistical Physics & Thermodynamics

Authors & Affiliations

Paul Ritchie1,* and Jan Sieber1,2,†

  • 1Centre for Systems, Dynamics and Control, College of Engineering, Mathematics and Physical Sciences, Harrison Building, University of Exeter, Exeter EX4 4QF, United Kingdom
  • 2EPSRC Centre for Predictive Modelling in Healthcare, University of Exeter, Exeter EX4 4QJ, United Kingdom

  • *pdlr201@exeter.ac.uk
  • J.Sieber@exeter.ac.uk

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Vol. 95, Iss. 5 — May 2017

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