Random Attractors of Stochastic Three-Component Reversible Gray-Scott System on Unbounded Domains

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

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

We consider the upper semicontinuity of the global random attractors for the stochastic three-component reversible Gray–Scott system on unbounded domains when the intensity of the noise converges to zero. 2013 Elsevier Inc. All rights reserved.

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

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 the Stochastic FitzHugh-Nagumo System on Unbounded Domains

The existence of a random attractor for the stochastic FitzHugh-Nagumo system defined on an unbounded domain is established. The pullback asymptotic compactness of the stochastic system is proved by uniform estimates on solutions for large space and time variables. These estimates are obtained by a cut-off technique.