| Abstract: |
| In this talk, we will describe recent analytical and computational tools to identify Most Probable Escape Paths (MPEPs) in stochastic dynamical systems (SDEs). The study of noise-induced tipping has been dominated by Freidlin-Wentzell (FW) theory. A downside of the FW theory is that it necessitates vanishingly small noise. However, for several applications of interest, particularly in environmental, biological or social contexts, intermediate noise is of more relevance. In focusing on the intermediate noise regime, the transient behavior of the underlying deterministic system will play a key role. We will thus use a dynamical system approach to identify MPEPs in SDEs. The Maslov index will help us distinguish which critical points of the FW functional are minimizers and help explain the effect of the interaction of noise and transient dynamics. The Onsager-Machlup (OM) functional, which is treated as a perturbation of the FW functional, will provide a selection mechanism to pick out a specific MPEP. Our computations will then be compared with Monte Carlo simulations in order to verify theoretical predictions. We will use a 2-dimensional autonomous system with a stable equilibrium solution coexisting with an unstable periodic orbit as a focal point for our methodology. |
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