Dynamical bifurcation for the Kuramoto–Sivashinsky equation

Abstract 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 A λ as λ crossed the first critical value λ 0 = 1 under the two cases. Our analysis was based on a new and mature attractor bifurcation theory developed by Ma and Wang (2005) [17] , [18] .