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arXiv · 2311.10231

Saddle avoidance of noise-induced transitions in multiscale systems

Reyk Börner·Ryan Deeley·Raphael Römer·Tobias Grafke·Valerio Lucarini·Ulrike Feudel
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Abstract

In multistable dynamical systems driven by weak Gaussian noise, transitions between competing states are often assumed to pass via a saddle on the separating basin boundary. By contrast, we show that timescale separation can cause saddle avoidance in non-gradient systems. Using toy models from neuroscience and ecology, we study cases where sample transitions deviate strongly from the instanton predicted by Freidlin-Wentzell theory, even for weak finite noise. We attribute this to a flat quasipotential and present an approach based on the Onsager-Machlup action to aptly predict transition paths.

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Reyk Börner, Ryan Deeley, Raphael Römer, Tobias Grafke, Valerio Lucarini, Ulrike Feudel. 2023-11-16. Saddle avoidance of noise-induced transitions in multiscale systems. https://doi.org/10.1103/physrevresearch.6.l042053

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