Synchronization of stochastic lattice equations

In this paper we consider a system of two coupled nonlinear lattice stochastic equations driven by additive white noise processes. We prove the master slave synchronization of the components of the coupled system, namely, for t→∞\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$t\rightarrow \infty $$\end{document} the solution of one of the subsystems (the slave component) converges to the values of a Lipschitz continuous function of the other component, the master component. To establish this kind of synchronization we will prove the existence of an exponentially attracting random invariant manifold for the coupled system.