Codimension-two bifurcation
= Codimension-two bifurcation
A codimension-two bifurcation requires two independent parameter conditions to hold simultaneously. Simultaneous stationary and <Hopf bifurcation> thresholds require both kinds of critical mode in the reduced <amplitude equation>. A crossing of modes at different <wavenumbers> is different from a zero-frequency double-zero degeneration of one fixed-wave-number cubic.