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

Tobias Grafke, Eric Vanden-Eijnden

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Article number093208
JournalJournal of Statistical Mechanics: Theory and Experiment
Issue number9
StatePublished - Sep 25 2017


  • active matter
  • large deviations in non-equilibrium systems
  • metastable states
  • stochastic processes

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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