Pitchfork region

The region of two-directed distillation (pitchfork region Regpuch) is located between the hne of the best product compositions (pitchfork distillation boundary) and boundary of distillation regions at infinite reflux Reg°° (Castillo et al., 1998 Davydyan, Malone, Doherty, 1997 Wahnschafft et al., 1992). 

Pitchfork region (Rogp c/i) region of concentration simplex where the section trajectory at certain reflux or reboil ratios leaves its own distillation region and comes into another distillation region. 

We note that split bifurcation regions and pitchfork bifurcation such as depicted in Figures 3.20 and 3.21 for Kc were never encountered by us for any fixed a in terms of yc. 

Fig. 6.2. Region of transverse stability for synchronous S and antisynchronous A CW solutions, respectively. P denotes the curves of transverse pitchfork bifurcations and H Hopf bifurcations for the parameters a = 2, J = 1, e = 0.03. (b) Zoom of the small part of (a) shows overlapping of the regions.

The last two roots x 2 and x 3 have imaginary components if Kp<3 and thus have no physical meaning in this region where x o is xmstable and x i stable. x 2 and x 3 become meaningful when p>3, a domain in which they are stable while x o and x i have become unstable. In the numerical example given in the text ( i=3.1), one observes an oscillation that "pitchforks" the value previously obtained ... 

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