It is restricted to positive pitchforks (simply because its negative version is of no use).
However, it is thus proved by the weakly nonlinear stability analysis that a supercritical pitchfork bifurcation occurs at the critical point.
We derive an amplitude equation to account for the imperfect pitchfork bifurcation.
There may of course be other factors which render the pitchfork bifurcation imperfect.
The rather short length of the vortex is characteristic of the disturbance for symmetrybreaking pitchfork bifurcations.
The pitchfork bifurcation in the symmetric problem is thereby disconnected.
In this subspace there is a pitchfork bifurcation giving rise to narrow transverse rolls.
The initial bifurcation (a pitchfork) gives rise to supercritical branches of diagonal rolls and small squares, of which only the latter are stable.
