Saddle avoidance of noise-induced transitions in multiscale systems

TL;DR

This paper investigates how timescale separation in multiscale systems can lead to saddle avoidance in noise-induced transitions, challenging traditional assumptions and providing a new predictive approach.

Contribution

It introduces a novel perspective on saddle avoidance caused by timescale separation and develops an Onsager-Machlup based method to predict transition paths.

Findings

Sample transitions deviate from instanton predictions in non-gradient systems.

Timescale separation causes saddle avoidance even with weak noise.

The Onsager-Machlup approach effectively predicts transition paths.

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.