O(2)-Hopf bifurcation for a model of cellular shock instability

We study by center manifold and normal form reduction an O(2)-Hopf bifurcation arising in a simplified model of bifurcating viscous shock waves in a channel, suppressing longitudinal dependence and modeling onset of instability via competing stable/unstable diffusions. For this canonical system, a cousin of the Kuramoto-Sivashinsky model, we are able to carry out a complete bifurcation analysis.