Steering most probable escape paths by varying relative noise intensities

We demonstrate the possibility to systematically steer the most probable escape paths (MPEPs) by adjusting the relative noise intensities in non-gradient dynamical systems that exhibit escape from a metastable point via a saddle point in the limit of small noise. Based on a geometric formulation of this escape process, an asymptotic theory is developed which is broadly applicable to fast-slow systems of two or more dimensions. In simple systems, our theory permits analytical expressions for the MPEPs and their associated minimum action values as a function of the relative noise intensities. These analytical predictions are in excellent agreement with computed MPEPs obtained using a geometric minimum action method (gMAM) [1], and both of these results are consistent with prehistory probability distributions obtained by direct simulation of the underlying stochastic differential equations. [1] M. Heymann and E. Vanden-Eijnden, Phys. Rev. Lett. $\mathbf{100}$, 140601 (2008).