Dynamic bifurcation of the n-dimensional complex Swift-Hohenberg equation

This paper is concerned with the bifurcation of a complex Swift-Hohenberg equation. The attractor bifurcation of the complex Swift-Hohenberg equation on a one dimensional domain (0, L) is investigated. It is shown that the n-dimensional complex Swift-Hohenberg equation bifurcates from the trivial solution to an attractor under the Dirichlet boundary condition on a general domain and under a periodic boundary condi tion when the bifurcation parameter crosses some critical values. The stability property of the bifurcation attractor is analyzed.