Metastability in randomly perturbed dynamical systems: beyond large-deviation theory
type: Item
instance of: scholarly article
title: Metastability in randomly perturbed dynamical systems: beyond large-deviation theory
zbMATH Open document ID: 1446.37055
DOI: 10.4171/197-1/5
author: Barbara Gentz
publication date: 2020-07-09T00:00:00Z
review text: Summary: We address the question of noise-induced transitions in continuous-time dynamical systems with special emphasis on aspects which go beyond standard large-deviation theory. After reviewing the classical Wentzell-Freidlin theory, we discuss the subexponential asymptotics of transition times between potential wells, transitions between stationary states in parabolic stochastic partial differential equations (SPDEs), first-exit from a domain with characteristic boundary, and the effect of noise on so-called mixed-mode oscillations. For the entire collection see [Zbl 1416.60012].
Mathematics Subject Classification ID: 37H30
Mathematics Subject Classification ID: 37H10
Mathematics Subject Classification ID: 37H20
zbMATH DE Number: 7219042
zbMATH Keywords: noise-induced transitions
zbMATH Keywords: large deviation theory
zbMATH Keywords: Wentzell-Freidlin theory
zbMATH Keywords: stochastic partial differential equations
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.4171/197-1/5
OpenAlex ID: W2952749556
cites work: Sharp asymptotics of metastable transition times for one dimensional SPDEs
cites work: Uniform estimates for metastable transition times in a coupled bistable system
cites work: Metastability in interacting nonlinear stochastic differential equations: I. From weak coupling to synchronization
cites work: Metastability in interacting nonlinear stochastic differential equations: II. Large-Nbehaviour
cites work: On the noise-induced passage through an unstable periodic orbit. I: Two-level model
cites work: Noise-Induced Phenomena in Slow-Fast Dynamical Systems
cites work: The Eyring-Kramers law for potentials with nonquadratic saddles
cites work: Sharp estimates for metastable lifetimes in parabolic SPDEs: Kramers law and beyond
cites work: On the Noise-Induced Passage through an Unstable Periodic Orbit II: General Case
cites work: Hunting French ducks in a noisy environment
cites work: From random Poincaré maps to stochastic mixed-mode-oscillation patterns
cites work: Galerkin Approximations for the Stochastic Burgers Equation
cites work: Metastability in reversible diffusion processes. I: Sharp asymptotics for capacities and exit times
cites work: Metastability in reversible diffusion processes. II: Precise asymptotics for small eigenvalues
cites work: Conditional exits for small noise diffusions with characteristic boundary
cites work: Cycling and skewing of exit measures for planar systems
cites work: Mixed-mode oscillations with multiple time scales
cites work: The Morris-Lecar neuron model embeds a leaky integrate-and-fire model
cites work: Large fluctuations for a nonlinear heat equation with noise
cites work: Random Perturbations of Dynamical Systems
cites work: Q5693588
cites work: Hypoelliptic estimates and spectral theory for Fokker-Planck operators and Witten Laplacians
cites work: Q4002114
cites work: Brownian motion in a field of force and the diffusion model of chemical reactions
cites work: Oscillatory Behavior of the Rate of Escape through an Unstable Limit Cycle
cites work: Synchronization: a universal concept in nonlinear sciences
cites work: Canards in \(\mathbb{R}^3\)
cites work: Random dynamics of the Morris–Lecar neural model
description: scientific article; zbMATH DE number 7219042