# Non-equilibrium transitions in multiscale systems with a bifurcating slow manifold

## TL;DR

This paper investigates noise-induced transitions in multiscale systems with bifurcating slow manifolds, revealing how bifurcation structures create reaction channels that significantly increase transition rates, with applications across biological, physical, and active matter systems.

## Contribution

It introduces a large deviation theory framework to analyze how bifurcations in slow manifolds facilitate rapid non-equilibrium transitions in multiscale systems.

## Key findings

- Bifurcation structures create reaction channels that enhance transition rates.
- Transitions are significantly affected by the slow manifold's bifurcation.
- Applications include models of insect outbreaks, phase separation, and active matter.

## Abstract

Noise-induced transitions between metastable fixed points in systems evolving on multiple time scales are analyzed in situations where the time scale separation gives rise to a slow manifold with bifurcation. This analysis is performed within the realm of large deviation theory. It is shown that these non-equilibrium transitions make use of a reaction channel created by the bifurcation structure of the slow manifold, leading to vastly increased transition rates. Several examples are used to illustrate these findings, including an insect outbreak model, a system modeling phase separation in the presence of evaporation, and a system modeling transitions in active matter self-assembly. The last example involves a spatially extended system modeled by a stochastic partial differential equation.