Dynamic Bifurcation of the Ginzburg-Landau Equation

We study in this article the bifurcation and stability of the solutions of the Ginzburg--Landau equation, using a notion of bifurcation called attractor bifurcation. We obtain in particular a full classification of the bifurcated attractor and the global attractor as $\lambda$ crosses the first critical value of the linear problem. Bifurcations from the rest of the eigenvalues of the linear problem are obtained as well.