Electronic Journal of Differential Equations, Vol. 2023 (2023), No. 20, pp. 1-22.

Title: Stochastic attractor bifurcation for the two-dimensional Swift-Hohenberg equation
 with multiplicative noise
       
Authors: Qingkun Xiao (Nanjing Agricultural Univ., Nanjing, China)
         Hongjun Gao (Southeast Univ., Nanjing, China)

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 L<sub>2</sub> and &sqrt;2L<sub>1</sub>
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.