A primer on noise-induced transitions in applied dynamical systems

TL;DR

This paper reviews the theory of noise-induced transitions in dynamical systems, emphasizing how weak noise can cause rare but critical events like state transitions or extinctions in physical and biological models.

Contribution

It provides an overview of the theoretical framework for understanding rare events caused by noise in stochastic dynamical systems, with illustrative applications.

Findings

Weak noise can induce large behavioral changes in systems.

Transitions between quasi-stable states are critical events influenced by noise.

Theoretical tools help quantify the likelihood of rare noise-induced events.

Abstract

Noise plays a fundamental role in a wide variety of physical and biological dynamical systems. It can arise from an external forcing or due to random dynamics internal to the system. It is well established that even weak noise can result in large behavioral changes such as transitions between or escapes from quasi-stable states. These transitions can correspond to critical events such as failures or extinctions that make them essential phenomena to understand and quantify, despite the fact that their occurrence is rare. This article will provide an overview of the theory underlying the dynamics of rare events for stochastic models along with some example applications.