Additive noise destroys the random attractor close to bifurcation

DOI10.1088/0951-7715/29/12/3934zbMath1357.60064arXiv1603.05500OpenAlexW2297052921MaRDI QIDQ2958861

Dirk Blömker, Luigi Amedeo Bianchi, Mei-Hua Yang

Publication date: 3 February 2017

Published in: Nonlinearity (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1603.05500

zbMATH Keywords

bifurcationunbounded domainsweighted spacesstationary solutionsrandom attractorrandom dynamical systemstochastic PDEsadditive noise

Mathematics Subject Classification ID

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Stability of topological dynamical systems (37B25) Attractors and their dimensions, Lyapunov exponents for infinite-dimensional dissipative dynamical systems (37L30) Stochastic partial differential equations (aspects of stochastic analysis) (60H15) Generation, random and stochastic difference and differential equations (37H10) Dynamical aspects of attractors and their bifurcations (37G35) Bifurcation theory for random and stochastic dynamical systems (37H20)

Related Items (8)

On the pitchfork bifurcation for the Chafee-Infante equation with additive noise ⋮ Non-explosion by Stratonovich noise for ODEs ⋮ Stochastic resonance in dissipative drift motion ⋮ The impact of multiplicative noise in SPDEs close to bifurcation via amplitude equations ⋮ Stochastic ODEs and stochastic linear PDEs with critical drift: regularity, duality and uniqueness ⋮ Modulation equation and SPDEs on unbounded domains ⋮ Continuity and topological structural stability for nonautonomous random attractors ⋮ The impact of white noise on a supercritical bifurcation in the Swift-Hohenberg equation

Cites Work

• Unnamed Item
• Random dynamics of the stochastic Boussinesq equations driven by Lévy noises
• Sufficient and necessary criteria for existence of pullback attractors for non-compact random dynamical systems
• Regularity of pullback random attractors for stochastic FitzHugh-Nagumo system on unbounded domains
• Random attractors for the stochastic FitzHugh-Nagumo system on unbounded domains
• Additive noise destroys a pitchfork bifurcation
• The dichotomy spectrum for random dynamical systems and pitchfork bifurcations with additive noise
• Exponentially stable stationary solutions for stochastic evolution equations and their perturba\-tion
• Random attractors for stochastic reaction-diffusion equations on unbounded domains
• Synchronization by noise for order-preserving random dynamical systems
• Collapse of attractors for ODEs under small random perturbations
• ASYMPTOTIC COMPACTNESS OF STOCHASTIC COMPLEX GINZBURG–LANDAU EQUATION ON AN UNBOUNDED DOMAIN
• Non-random Invariant Sets for Some Systems of Parabolic Stochastic Partial Differential Equations
• The effect of noise on the Chafee-Infante equation: A nonlinear case study
• Order-preserving random dynamical systems: equilibria, attractors, applications
• Attractors for modulation equations on unbounded domains-existence and comparison
• Modulation Equation for Stochastic Swift--Hohenberg Equation
• Tempered random attractors for parabolic equations in weighted spaces

This page was built for publication: Additive noise destroys the random attractor close to bifurcation