Well-posedness and dynamics of fractional FitzHugh-Nagumo systems on \(\mathbb{R}^N\) driven by nonlinear noise

DOI10.1007/s11425-019-1714-2zbMath1482.37078OpenAlexW3083353710MaRDI QIDQ2243563

Renhai Wang, Bixiang Wang, Bo-ling Guo

Publication date: 11 November 2021

Published in: Science China. Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11425-019-1714-2

zbMATH Keywords

unbounded domaininvariant measurenonlinear noiseweak pullback mean random attractorfractional FitzHugh-Nagumo system

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Attractors (35B41) Attractors and their dimensions, Lyapunov exponents for infinite-dimensional dissipative dynamical systems (37L30) Infinite-dimensional random dynamical systems; stochastic equations (37L55)

Related Items (24)

Asymptotic behavior of non-autonomous Lamé systems with subcritical and critical mixed nonlinearities ⋮ Weak pullback mean random attractors for the stochastic convective Brinkman–Forchheimer equations and locally monotone stochastic partial differential equations ⋮ Existence and approximation of attractors for nonlinear coupled lattice wave equations ⋮ Existence, exponential mixing and convergence of periodic measures of fractional stochastic delay reaction-diffusion equations on \(\mathbb{R}^n\) ⋮ Asymptotically autonomous dynamics for fractional subcritical nonclassical diffusion equations driven by nonlinear colored noise ⋮ On solutions of linear and nonlinear fractional differential equations with application to fractional order RC type circuits ⋮ Random attractors and invariant measures for 3D stochastic globally modified Navier-Stokes equations with time-dependent delay and coefficient ⋮ Random attractors and invariant measures for stochastic convective Brinkman-Forchheimer equations on 2D and 3D unbounded domains ⋮ Stochastic 3D globally modified Navier-Stokes equations: weak attractors, invariant measures and large deviations ⋮ Random dynamics and limiting behaviors for 3D globally modified Navier–Stokes equations driven by colored noise ⋮ Random attractor, invariant measures, and ergodicity of lattice \(p\)-Laplacian equations driven by superlinear noise ⋮ Dynamics of the stochastic \(g\)-Navier-Stokes equations driven by nonlinear noise ⋮ Mean attractors and invariant measures of locally monotone and generally coercive SPDEs driven by superlinear noise ⋮ Global well-posedness, mean attractors and invariant measures of generalized reversible Gray-Scott lattice systems driven by nonlinear noise ⋮ Evolution systems of probability measures for nonautonomous Klein-Gordon Itô equations on \(\mathbb{Z}^N\) ⋮ Invariant measures and stochastic Liouville type theorem for non-autonomous stochastic reaction-diffusion equations ⋮ Asymptotically Autonomous Robustness in Probability of Random Attractors for Stochastic Navier-Stokes Equations on Unbounded Poincaré Domains ⋮ Limiting dynamics for stochastic FitzHugh-Nagumo lattice systems in weighted spaces ⋮ New results for convergence problem of fractional diffusion equations when order approach to \(1^-\). ⋮ Dynamics for subcritical fractional nonclassical diffusion equations with nonlinear Wong-zakai noise and delays ⋮ Random dynamics of non-autonomous fractional stochastic \(p\)-Laplacian equations on \(\mathbb{R}^N\) ⋮ Long-time dynamics of fractional nonclassical diffusion equations with nonlinear colored noise and delay on unbounded domains ⋮ Limit measures and ergodicity of fractional stochastic reaction–diffusion equations on unbounded domains ⋮ Dynamics of stochastic Ginzburg–Landau equations driven by nonlinear noise

Cites Work

• Unnamed Item
• Unnamed Item
• Existence and uniqueness of invariant measures for stochastic reaction-diffusion equations in unbounded domains
• Mean-square random dynamical systems
• Sufficient and necessary criteria for existence of pullback attractors for non-compact random dynamical systems
• Hitchhiker's guide to the fractional Sobolev spaces
• Regularity of pullback random attractors for stochastic FitzHugh-Nagumo system on unbounded domains
• Dynamics of the 3-D fractional complex Ginzburg-Landau equation
• Random attractors for a class of stochastic partial differential equations driven by general additive noise
• Ergodicity of the infinite dimensional fractional Brownian motion
• On the stochastic Benjamin--Ono equation
• Asymptotic behavior of stochastic fractional power dissipative equations on \(\mathbb{R}^n\)
• Non-autonomous and random attractors for delay random semilinear equations without uniqueness
• Random attractors for quasi-continuous random dynamical systems and applications to stochastic reaction-diffusion equations
• Attractors for random dynamical systems
• Random attractors
• A variational approach to dissipative SPDEs with singular drift
• Asymptotic behavior of random FitzHugh-Nagumo systems driven by colored noise
• Invariant measure for the stochastic Navier-Stokes equations in unbounded 2D domains
• Regularity of random attractors for fractional stochastic reaction-diffusion equations on \(\mathbb{R}^n\)
• Pullback attractors of nonautonomous and stochastic multivalued dynamical systems
• Random attractors for degenerate stochastic partial differential equations
• Asymptotic behaviour of a stochastic semilinear dissipative functional equation without uniqueness of solutions
• Continuity and random dynamics of the non-autonomous stochastic FitzHugh-Nagumo system on \(\mathbb{R}^N\)
• Dynamics of fractional stochastic reaction-diffusion equations on unbounded domains driven by nonlinear noise
• Weak pullback attractors for mean random dynamical systems in Bochner spaces
• Asymptotic behavior of non-autonomous fractional stochastic reaction-diffusion equations
• Random attractors for stochastic reaction-diffusion equations on unbounded domains
• Limiting behavior of dynamics for stochastic reaction-diffusion equations with additive noise on thin domains
• Asymptotic behavior of stochastic Fitzhugh-Nagumo systems on unbounded thin domains
• Random dynamics of fractional nonclassical diffusion equations driven by colored noise
• On the stochastic Burgers equation with a polynomial nonlinearity in the real line
• Invariant measures for stochastic nonlinear beam and wave equations
• Random attractors for singular stochastic evolution equations
• Invariant measures for stochastic partial differential equations in unbounded domains
• RANDOM DIFFERENTIAL EQUATIONS WITH RANDOM DELAYS
• Asymptotic behavior of fractional nonclassical diffusion equations driven by nonlinear colored noise on $\mathbb{R}^N$
• Flattening, squeezing and the existence of random attractors
• Invariant measures for a stochastic nonlinear Schroedinger equation
• Nonequilibrium scaling limit for a tagged particle in the simple exclusion process with long jumps
• Stochastic evolution equations
• Uniqueness of the invariant measure for a stochastic PDE driven by degenerate noise
• Stochastic Equations in Infinite Dimensions

This page was built for publication: Well-posedness and dynamics of fractional FitzHugh-Nagumo systems on \(\mathbb{R}^N\) driven by nonlinear noise