Stochastic attractor bifurcation for the two-dimensional Swift-Hohenberg equation with multiplicative noise
DOI:
https://doi.org/10.58997/ejde.2023.20Abstract
This article concerns the dynamical transitions of the stochastic Swift-Hohenberg equation with multiplicative noise on a two-dimensional domain (-L,L) times (-L, L). With α and L regarded as parameters, we show that the approximate reduced system corresponding to the invariant manifold undergoes a stochastic pitchfork bifurcation near the critical points, and the impact of noise on stochastic bifurcation of the Swift-Hohenberg equation. We find the approximation representation of the manifold and the corresponding reduced systems for stochastic Swift-Hohenberg equation when L2 and √2L1 are close together.
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