An approach for the analysis of spacially localized oscillations

Abstract

The dynamics near a strange fixed point arising in the Kuramoto-Sivashinsky equation are investigated as the equation undergoes a Hopf bifurcation and then further bifurcates to a modulated wave. While the representation of the spatial structures generated requires a relatively broad fourier spectrum we show that the essential features are captured by 3 eigenfunctions of the time averaged correlation matrix. At the Hopf bifurcation point, the eigenfunctions correspond to the fixed point and the 2 unstable directions of the center eigenspace.