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 \(t\rightarrow \infty \) 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.

中文翻译：

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随机晶格方程的同步

在本文中，我们考虑了由加性白噪声过程驱动的两个耦合的非线性晶格随机方程组。我们证明了耦合系统组件的主从同步，即对于\（t \ rightarrow \ infty \），一个子系统（从组件）的解收敛于另一个子系统的Lipschitz连续函数的值组件，主组件。为了建立这种同步，我们将证明耦合系统存在指数吸引随机不变流形。