Stochastic attractor bifurcation for the two-dimensional Swift-Hohenberg equation with multiplicative noise
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Date
2023-02-27
Authors
Xiao, Qingkun
Gao, Hongjun
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
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.
Description
Keywords
Swift-Hohenberg equation, Stochastic bifurcation, Dynamical transition, Parameterizing manifold
Citation
Xiao, 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.
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Attribution 4.0 International
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This work is licensed under a Creative Commons Attribution 4.0 International License.