Hi all,

In the weakly nonlinear stability analysis, the center manifold reduction can be used to study the first linear bifurcation. This lead to the Ginzburg-Landau equation

$\displaystyle \frac{\partial A}{\partial t}=a_1A + a_3 A^*A^2 + a_5 A^{*2}A^3 + ...... $

I have several questions.

Is the center manifold corresponding to the space $\displaystyle a_1=0$? I feel this because at the linear bifurcation, the growth rate of the disturbance is zero, which implies that $\displaystyle a_1=0$ in the above equation.

Then does there exist a submanifold corresponding to $\displaystyle a_3=0$?

Thanks a lot.