We consider the impact of additive Gaussian white noise on a supercritical pitchfork bifurcation in an unbounded domain. As an example we focus on the stochastic Swift–Hohenberg equation with polynomial nonlinearity. Here we identify the order where small noise first impacts the bifurcation. Using an approximation via modulation equations, we provide a tool to analyse how the noise influences the dynamics close to a change of stability.

中文翻译：

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Swift–Hohenberg方程中白噪声对超临界分叉的影响

我们考虑加性高斯白噪声对无界域中超临界干草叉分叉的影响。作为示例，我们关注具有多项式非线性的随机Swift–Hohenberg方程。在这里，我们确定了小噪声首先影响分叉的顺序。使用通过调制方程式的近似值，我们提供了一种工具来分析噪声如何影响接近稳定性变化的动力学。