Applied Mathematics Commons^™

A Primer On Noise-Induced Transitions In Applied Dynamical Systems, Eric Forgoston, Richard O. Moore

Department of Applied Mathematics and Statistics Faculty Scholarship and Creative Works

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 …