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.

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 the Stochastic Discrete Long Wave-Short Wave Resonance Equations

We prove the existence of the random attractor for the stochastic discrete long wave-short wave resonance equations in an infinite lattice. We prove the asymptotic compactness of the random dynamical system and obtain the random attractor.

SPOT PATTERNS IN GRAY SCOTT MODEL WITH APPLICATION TO EPIDEMIC CONTROL

In this work, we analyse a pair of two-dimensional coupled reaction-diusion equations known as the Gray-Scott model, in which spot patterns have been observed. We focus on stationary patterns, and begin by deriving the asymptotic scaling of the parameters and variables necessary for the analysis of these patterns. A complete bifurcation study of these solutions is presented. The main mathematic...