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arXiv · 2005.09676

The impact of white noise on a supercritical bifurcation in the Swift-Hohenberg equation

Luigi Amedeo Bianchi·Dirk Blömker
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Abstract

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.

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Luigi Amedeo Bianchi, Dirk Blömker. 2020-05-19. The impact of white noise on a supercritical bifurcation in the Swift-Hohenberg equation. https://doi.org/10.1016/j.physd.2020.132742

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