Inverse-square law between time and amplitude for crossing tipping thresholds.

ABSTRACT: A classical scenario for tipping is that a dynamical system experiences a slow parameter drift across a fold tipping point, caused by a run-away positive feedback loop. We study what happens if one turns around after one has crossed the threshold. We derive a simple criterion that relates how far the parameter exceeds the tipping threshold maximally and how long the parameter stays above the threshold to avoid tipping in an inverse-square law to observable properties of the dynamical system near the fold. For the case when the dynamical system is subject to stochastic forcing we give an approximation to the probability of tipping if a parameter changing in time reverses near the tipping point. The derived approximations are valid if the parameter change in time is sufficiently slow. We dem

SUBMITTER: Ritchie P 

PROVIDER: S-EPMC6405451 | biostudies-literature | 2019 Feb

REPOSITORIES: biostudies-literature