The Poincaré maps of a slow-fast stochastic system

DOI10.1016/j.jde.2022.11.027OpenAlexW4310015217MaRDI QIDQ2106549

Min Yang, Guanggan Chen

Publication date: 16 December 2022

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jde.2022.11.027

zbMATH Keywords

Poincaré mapgeometric distributionexit problemrandom manifoldslow-fast stochastic system

Mathematics Subject Classification ID

Geometric probability and stochastic geometry (60D05) Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Generation, random and stochastic difference and differential equations (37H10) Periodic orbits of vector fields and flows (37C27) Invariant manifold theory for dynamical systems (37D10) Systems with slow and fast motions for nonlinear problems in mechanics (70K70)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A new model for realistic random perturbations of stochastic oscillators
• The Poincaré map of randomly perturbed periodic motion
• Sharp estimates for metastable lifetimes in parabolic SPDEs: Kramers law and beyond
• First-passage failure of MDOF nonlinear oscillator
• Hunting French ducks in a noisy environment
• Multiple time scale dynamics
• Slow manifold and averaging for slow-fast stochastic differential system
• A stochastic return map for stochastic differential equations
• The Poisson kernel for certain degenerate elliptic operators
• First-passage failure of quasi-non-integrable-Hamiltonian systems
• Conditional exits for small noise diffusions with characteristic boundary
• Random difference equations and renewal theory for products of random matrices
• Invariant manifolds for stochastic partial differential equations.
• Smooth stable and unstable manifolds for stochastic evolutionary equations
• Geometric singular perturbation theory for stochastic differential equations.
• From random Poincaré maps to stochastic mixed-mode-oscillation patterns
• Invariant manifolds for random dynamical systems with slow and fast variables
• Mixed-mode oscillations and interspike interval statistics in the stochastic FitzHugh–Nagumo model
• The Integral of a Symmetric Unimodal Function over a Symmetric Convex Set and Some Probability Inequalities
• Mixed-Mode Oscillations in Three Time-Scale Systems: A Prototypical Example
• Bursting Oscillations Induced by Small Noise
• Parabolic Bursting in an Excitable System Coupled with a Slow Oscillation
• Random Perturbations of Reaction-Diffusion Equations: The Quasi-Deterministic Approximation
• Large fluctuations for a nonlinear heat equation with noise
• The asymptotic completeness of inertial manifolds
• Mathematical Modeling in Continuum Mechanics
• On the exponential exit law in the small parameter exit problem
• Unfoldings of Singular Hopf Bifurcation
• Noise-Induced Phenomena in Slow-Fast Dynamical Systems
• On the Noise-Induced Passage through an Unstable Periodic Orbit II: General Case
• Stochastic differential equations. An introduction with applications.