A rate-induced tipping in the Pearson diffusion

TL;DR

This paper investigates how rate-induced tipping occurs in Pearson diffusion processes and demonstrates that noise accelerates the escape of solutions from the bounded domain.

Contribution

It introduces the analysis of rate-induced tipping in Pearson diffusions and shows the effect of noise on escape speed, expanding understanding of stochastic tipping phenomena.

Findings

Noise accelerates escape from the domain.

Solutions escape in finite time under rate-induced tipping.

Noise-free solutions stay bounded under certain conditions.

Abstract

Rate-induced tipping is an instability that occurs in a system when its time-dependent rate parameter becomes larger than a threshold value. We investigate a Pearson diffusion process, a diffusion process having solutions staying in a bounded domain under certain conditions, whose noise-free limit experiences a rate-induced tipping such that solutions escape from the domain in a finite time. We show that the existence of noise leads to faster escapement from the domain.