Saddle avoidance of noise-induced transitions in multiscale nonequilibrium systems*

In multistable dynamical systems driven by weak Gaussian noise, transitions between competing attracting states are commonly expected to pass near a saddle on the separating basin boundary. However, we show that nonequilibrium systems can behave quite differently: timescale separation can cause saddle avoidance. Using toy models from neuroscience and ecology, we analyze cases where sample transition paths deviate strongly from the minimum action path (instanton) predicted by large deviation theory, even for weak noise. As a result, the sample transition paths cross the basin boundary far away from the saddle. We attribute this to a flat Freidlin-Wentzell quasipotential and propose an approach based on the Onsager-Machlup action to accurately predict the most probable transition path. Anticipating the path of critical transitions in state space is desirable in applications ranging from brain dynamics to lasers and abrupt climate change, as it offers insight into the physical transition mechanism.