A primer on noise-induced transitions in applied dynamical systems

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.

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• A Dynamical Systems Approach for Most Probable Escape Paths over Periodic Boundaries
• Quantum pure noise-induced transitions: A truly nonclassical limit cycle sensitive to number parity
• Large and small fluctuations in oscillator networks from heterogeneous and correlated noise
• Noise-induced peak intensity fluctuations in class B laser systems