College of Sciences
Nanjing Agricultural University
Nanjing 210095, China
email: xiaoqk@njau.edu.cn
School of Mathematics
Southeast University
Nanjing 211189, China
email: hjgao@seu.edu.cn
Qingkun Xiao, Hongjun Gao
Abstract:
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
Show me the PDF file (388 KB), TEX file for this article.
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Qingkun Xiao College of Sciences Nanjing Agricultural University Nanjing 210095, China email: xiaoqk@njau.edu.cn |
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| Hongjun Gao School of Mathematics Southeast University Nanjing 211189, China email: hjgao@seu.edu.cn |
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