In this paper, a spatially extended stochastic reaction–diffusion model is studied. Due to Turing instability, stable nonhomogeneous stationary patterns are generated in such models. A theoretical approach to estimating the mean-square deviation of random solutions from the stable deterministic pattern–attractor is demonstrated. Stochastic sensitivity functions for stable stationary patterns are introduced. Theoretical evaluations are compared with statistically obtained data. Based on this approach, we investigate stochastic properties of different patterns in Brusselator. Variations in pattern sensitivity to noise and phenomenon of stochastic preference are discussed.

中文翻译：

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空间扩展系统中平稳模式的随机敏感性分析

在本文中，研究了空间扩展的随机反应-扩散模型。由于图灵不稳定性，在这些模型中会生成稳定的非齐次平稳模式。演示了一种从稳定的确定性模式吸引器估计随机解的均方偏差的理论方法。介绍了稳定平稳模式的随机灵敏度函数。将理论评估与统计获得的数据进行比较。基于这种方法，我们研究了 Brusselator 中不同模式的随机特性。讨论了对噪声和随机偏好现象的模式敏感性的变化。