Saddle avoidance

When noise kicks you where you wouldn't expect

This work elucidates the effect of timescale separation on transition paths in multistable, noise-driven dynamical systems, and proposes a correction to what is predicted using large deviation theory in the presence of multiple timescales.

Saddle points are widely understood as gateways for noise-induced transitions between the competing attractors of random multistable systems. Based on this viewpoint, supported by the least-action principle of Freidlin-Wentzell theory, the properties of saddles are often used to deduce insight into the transition behavior, including transition rates and mechanisms. However, we show that timescale separation can cause saddle avoidance: transition paths may deviate from the minimizer of the Freidlin-Wentzell action and bypass the saddle for noise of weak but finite intensity.

Since most real systems of interest feature multiple timescales and non-vanishing noise, this discovery challenges the generic role of saddles and the relevance of classical applications of large deviation theory for the prediction of most probable transition paths. Our results illustrate conditions that lead to saddle avoidance and offer a solution approach for predicting transition paths in this case.

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