Most Probable Tipping Events in Stochastically Perturbed Fillippov Systems
Recently there has been considerable interest in understanding tipping events within the Earth’s climate system. In particular, extreme levels of green house gas emissions pose a serious threat to the stability of Arctic sea ice. One mechanism for tipping is so called noise induced tipping in which stochastic perturbations cause the system to transition between (meta)stable states. For smooth autonomous dynamical systems, the Freidlin-Wentzell (FW) theory of large deviations provides a robust framework for computing such transitions as minimizers of an action functional. However, classical FW theory is not valid for piecewise smooth systems or systems with non-autonomous periodic forcing; precisely the type of systems commonly used as conceptual models for climate systems. In this talk I will discuss our work in extending the FW theory to such nonstandard systems using tools from dynamical systems and variational calculus. Along the way I will present an introduction to the FW theory of large deviations, Fillippov dynamical systems, and the necessary tools from calculus of variations.