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.

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 on Infinite Lattices

Perturbation of Stochastic Boussinesq Equations with Multiplicative White Noise

The Boussinesq equation is a mathematics model of thermohydraulics, which consists of equations of fluid and temperature in the Boussinesq approximation.The deterministic case has been studied systematically by many authors (e.g., see [1– 3]). However, in many practical circumstances, small irregularity has to be taken into account.Thus, it is necessary to add to the equation a random force, wh...

A pr 2 01 4 Sufficient Criteria for Existence of Pullback Attractors for Stochastic Lattice Dynamical Systems with Deterministic Non - autonomous Terms

We consider the pullback attractors for non-autonomous dynamical systems generated by stochastic lattice differential equations with non-autonomous deterministic terms. We first establish a sufficient condition for existence of pullback attractors of lattice dynamical systems with both non-autonomous deterministic and random forcing terms. As an application of the abstract theory, we prove the ...