Electron. J. Differential Equations, Vol. 2023 (2023), No. 20, pp. 1-22.

Stochastic attractor bifurcation for the two-dimensional Swift-Hohenberg equation with multiplicative noise

Qingkun Xiao, Hongjun Gao

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.

Submitted December 30, 2022. Published February 27, 2023.
Math Subject Classifications: 35B40, 35B41, 37H20, 37L55.
Key Words: Swift-Hohenberg equation; stochastic bifurcation; dynamical transition; parameterizing manifold.
DOI: https://doi.org/10.58997/ejde.2023.20

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Qingkun Xiao
College of Sciences
Nanjing Agricultural University
Nanjing 210095, China
email: xiaoqk@njau.edu.cn
  Hongjun Gao
School of Mathematics
Southeast University
Nanjing 211189, China
email: hjgao@seu.edu.cn

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