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  • Letter
  • Open Access

Saddle avoidance of noise-induced transitions in multiscale systems

Reyk Börner1,*,†, Ryan Deeley2,*,‡, Raphael Römer3, Tobias Grafke4, Valerio Lucarini5, and Ulrike Feudel2

  • *These authors contributed equally to this work.
  • †Contact author: reyk.boerner@reading.ac.uk
  • ‡Contact author: ryan.deeley@uni-oldenburg.de
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Phys. Rev. Research 6, L042053 – Published 2 December, 2024

DOI: https://doi.org/10.1103/PhysRevResearch.6.L042053

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 nongradient systems. Using toy models from neuroscience and ecology, we study cases where sample transitions deviate strongly from the instanton predicted by the 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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Phys. Rev. Research 6, L042053– Published 2 December, 2024
  • Received 16 November 2023
  • Revised 11 June 2024
  • Accepted 7 October 2024
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