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.

References in corpus (5)

• The large deviation approach to statistical mechanics
• Extinction Rates for Fluctuation-Induced Metastabilities : A Real-Space WKB Approach
• Disease extinction in the presence of non-Gaussian noise
• A variational approach to probing extreme events in turbulent dynamical systems
• Probabilistic response and rare events in Mathieu's equation under correlated parametric excitation

Cited by in corpus (18)

• Extreme events in dynamical systems and random walkers: A review
• Using reservoir computer to predict and prevent extreme events
• Dynamics of a stochastic excitable system with slowly adapting feedback
• Predicting Critical Transitions in Multiscale Dynamical Systems Using Reservoir Computing
• Rate and Noise-Induced Tipping Working in Concert
• Two paradigmatic scenarios for inverse stochastic resonance
• Noise-induced tipping under periodic forcing: preferred tipping phase in a non-adiabatic forcing regime
• Most probable transition paths in piecewise-smooth stochastic differential equations
• Universality of noise-induced resilience restoration in spatially-extended ecological systems
• Swimmer dynamics in externally-driven fluid flows: The role of noise
• Precursors to Rare Events in Stochastic Resonance
• Stochastic ejection of nanocontact droplet solitons via drift instability
• Nonadiabatic escape and stochastic resonance
• Controlling mean exit time of stochastic dynamical systems based on quasipotential and machine learning
• 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