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

Electronic Journal of Differential Equations

article

Qingkun Xiao¹  Hongjun Gao² 

[1] College of Sciences Nanjing Agricultural University Nanjing 210095;School of Mathematics Southeast University Nanjing 211189

关键词: Swift-Hohenberg equation;    stochastic bifurcation;    dynamical transition;    parameterizing manifold;   

DOI  :  10.58997/ejde.2023.20

学科分类：数学（综合）

来源: Texas State University

【 摘 要 】

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.

【 授权许可】

CC BY