Probability of noise- and rate-induced tipping
Physical Review E
American Physical Society
©2017 American Physical Society
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.
P.D.L.R.’s research was supported by funding from the EPSRC Grant EP/M008495/1, J.S. research was supported by funding from the EPSRC Grant EP/N023544/1 and by funding from the European Union’s Horizon 2020 research and innovation programme under Grant Agreement number 643073.
This is the author accepted manuscript. The final version is available from American Physical Society via the DOI in this record.
Vol. 95, 052209