Box 4—figure 1. Schematic description of possible ways in which primary bifurcating traveling waves (TW) and standing waves (SW) can emerge from the finite wavenumber Hopf bifurcation.

Solid (dashed) lines indicate stable (unstable) solutions of a certain state variable (modified from Knobloch, 1986). The left insets demonstrate space-time plots of typical forms of SW employing no-flux boundary conditions (top) and TW employing periodic boundary conditions (bottom) that emerge from super-critical bifurcations.