Xiao, QingkunGao, Hongjun2023-05-232023-05-232023-02-27Xiao, Q., & Gao, H. (2023). Stochastic attractor bifurcation for the two-dimensional Swift-Hohenberg equation with multiplicative noise. <i>Electronic Journal of Differential Equations, 2023</i>(20), pp. 1-22.1072-6691https://hdl.handle.net/10877/16855This 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.Text22 pages1 file (.pdf)enAttribution 4.0 InternationalSwift-Hohenberg equationStochastic bifurcationDynamical transitionParameterizing manifoldArticleThis work is licensed under a Creative Commons Attribution 4.0 International License.