69 citations · 178 across the 4 of their papers we have counts for
4 papers · 1 filter
Inverse-square law between time and amplitude for crossing tipping thresholds
Paul Ritchie, Ozkan Karabacak, Jan Sieber
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 wh…
Early-warning indicators in the dynamic regime
Paul Ritchie, Jan Sieber
Early-warning indicators (increase of autocorrelation and variance) are commonly applied to time series data to try and detect tipping points of real-world systems. The theory behi…
Probability of noise- and rate-induced tipping
Paul Ritchie, Jan Sieber
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 sma…
Early-warning indicators for rate-induced tipping
Paul Ritchie, Jan Sieber
A dynamical system is said to undergo rate-induced tipping when it fails to track its quasi-equilibrium state due to an above-critical-rate change of system parameters. We study a…