In this paper, a problem of the analysis of the randomly forced patterns in spatially distributed systems with diffusion is considered. For the approximation of mean-square deviations of random solutions from the unforced deterministic pattern-attractors, we suggest a constructive method based on the stochastic sensitivity technique. To demonstrate an efficiency of this method, we consider the Levin-Segel model with formation of non-homogeneous structures of the phytoplankton and herbivore populations. The spatial peculiarities of probabilistic distributions near patterns are investigated. The dependence of the stochastic sensitivity on the variation of system parameters is studied. An application of the stochastic sensitivity technique to the study of noise-induced transitions between coexisting spatial structures is demonstrated.

在本文中，考虑了具有扩散的空间分布系统中随机强制模式的分析问题。对于来自非强制确定性模式吸引子的随机解的均方偏差的近似值，我们提出了一种基于随机灵敏度技术的构造方法。为了证明这种方法的效率，我们考虑了浮游植物和食草动物种群的非均质结构形成的 Levin-Segel 模型。研究了模式附近概率分布的空间特性。研究了随机灵敏度对系统参数变化的依赖性。展示了随机灵敏度技术在研究共存空间结构之间的噪声引起的过渡中的应用。