Bifurcation and of the Generalized Complex Ginzburg–landau Equation

We study in this paper the bifurcation and stability of the solutions of the complex Ginzburg–Landau equation(CGLE). We investigate two different modes of CGLE. We study the first mode of CGLE which has only cubic unstable nonlinear term and later we also study the second mode of CGLE which has both cubic and quintic nonlinear terms. The solutions considered in cubic CGLE bifurcate from the trivial state supercritically in some parameter range. However, for the cubic-quintic CGLE, solutions bifurcate from the trivial state subcritically. Due to the global attractor, we achieved a saddle node bifurcation point λc. We also study the steady state bifurcation of the CGLE and verify that the bifurcated invariant sets Σk contain steady state solutions.