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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.
Each pitchfork occurring in the design is the conclusion of a unique rule among those given below.
The case 0 (1) > 0 is usually referred to as a subcritical pitchfork bifurcation, and the case 0 (1) < 0 as a supercritical pitchfork bifurcation.
This stability is finally transferred to spatially modulated two-dimensional rolls in another pitchfork bifurcation.
On the other hand, the amplitude equation (2.31) directly expresses the pitchfork bifurcation at the critical state.
This is the so-called pitchfork bifurcation which determines the incidence of three-dimensional wave motions.
Moreover, it does not fall into any pitchfork class known.
Depending on the way we use them, pitchforks can be streamlike or anti-streamlike.
