Dynamical bifurcation for the Kuramoto–Sivashinsky equation

In this paper, by using the center manifold reduction method, together with the eigenvalue analysis, we made bifurcation analysis for the Kuramoto–Sivashinsky equation, and proved that the Kuramoto–Sivashinsky equation with constraint condition bifurcates an attractor AλAλ as λλ crossed the first critical value λ0=1λ0=1 under the two cases. Our analysis was based on a new and mature attractor bifurcation theory developed by Ma and Wang (2005) [17] and [18].