Katherine Slyman

Title: The Interplay of Rate and Noise Tipping and Applications

Abstract.  We present a theory for understanding tipping events in low-dimensional dynamical systems with additive noise and time-dependent parameters, whose interplay results in a large increase in the frequency of tipping. While rate-induced tipping does not require any random fluctuations within the system, the ramp parameter and added noise can conspire to cause tipping of the system below the critical rate. Building on the work of Ritchie and Sieber (2016), who considered rates close to the critical rate, we first consider a one-dimensional differential equation with additive noise and a ramp parameter. In this model, using the Fredlin-Wentzell theory, we show that there exists a heteroclinic connection in extended phase space between equilibria for all rates less than the critical rate. This heteroclinic orbit is a minimizer of the Freidlin-Wentzell functional and thus corresponds to the most probable path between these two points. We construct this most probable path using geometric dynamical systems methods, as well as present numerical simulations for verification and visualization of this most probable path.