Noise-Induced Escape From an Attractor
The analysis of the exit problem, as defined in Section 6.4 and analyzed in Chapter 6, was based on explicit integral representations of solutions to the one-dimensional Andronov–Vitt–Pontryagin boundary value problems (6.33) for the exit distribution and for the MFPT. Such representations are in general unavailable in higher dimensions so that there is no obvious generalization of these methods for the exit problem in higher dimensions. Another approach, that is based on constructing an asymptotic solution to the boundary value problems by the methods of singular perturbations, can be generalized to higher dimensions (see Section 10.2).
KeywordsBoundary Layer Saddle Point Exit Point Boundary Layer Equation Eikonal Equation
Unable to display preview. Download preview PDF.