Upper semicontinuity of random attractors for stochastic three-component reversible Gray-Scott system

Random Attractors for Stochastic Three-Component Reversible Gray-Scott System on Infinite Lattices

Random Attractors for Stochastic Lattice Reversible Gray-scott Systems with Additive Noise

In this article, we prove the existence of a random attractor of the stochastic three-component reversible Gray-Scott system on infinite lattice with additive noise. We use a transformation of addition involved with Ornstein-Uhlenbeck process, for proving the pullback absorbing property and the pullback asymptotic compactness of the reaction diffusion system with cubic nonlinearity.

Random Attractors for Stochastic Three-Component Reversible Gray-Scott System with Multiplicative White Noise

Upper Semicontinuity of Random Attractors for Non-compact Random Dynamical Systems

The upper semicontinuity of random attractors for non-compact random dynamical systems is proved when the union of all perturbed random attractors is precompact with probability one. This result is applied to the stochastic Reaction-Diffusion with white noise defined on the entire space Rn.

upper semicontinuity of attractors for small random perturbations of dynamical systems

The relationship between random attractors and global attractors for dynamical systems is studied. If a partial differential equation is perturbed by an −small random term and certain hypotheses are satisfied, the upper semicontinuity of the random attractors is obtained as goes to zero. The results are applied to the Navier-Stokes equations and a problem of reaction-diffusion type, both pertur...