Gluing bifurcation

Figure 5. Bifurcation diagram on the plane of the two control parameters p and a. The solid lines 1 and 2 mark the primary instability, where the homogeneous homeotropic orientation becomes unstable. At 1, the bifurcation is a stationary (pitchfork) bifurcation, and a Hopf one at 2. The two lines connect in the Takens-Bogdanov (TB) point. The solid lines 3 and 4 mark the first gluing bifurcation and the second gluing bifurcation respectively. The dashed lines 2b and 3b mark the lines of the primary Hopf bifurcation and the first gluing bifurcation when calculated without the inclusion of flow in the equations.

Figure 12.15 A gluing bifurcation leading to compound oscillation. Successive frames represent phase portraits in concentration space for different sets of constraint parameters.

Meron, E. Procaccia, I. 1987. Gluing Bifurcations in Critical Flows The Route to Chaos in Parametrically Excited Surface Waves, Phys. Rev. A 35, 4008-4011. 

Figure 5.5 — Flow-through biosensor for the determination of L-glutamate. (A) Flow injection manifold. (B) Sensing microzone of the probe sensor (optrode), incorporated in the flow-cell (FTC). P pump IV injection valve MC mixing chamber AD air damper BFB bifurcated fibre bimdle LS light source PMT photomultiplier R recorder GLU L-glutamate 0-Glu 2-oxoglutarate E enzyme layer I optical insulator S sensing layer PS polyester support. For details, see text. (Adapted from [6] with permission of Elsevier Science Publishers).

Figure 10 shows the proposed ubiquinol oxidation and electron bifurcation mechanism at Qp site. (A) In the absence of the ubiquinone, the side chain of Glu-271 is connected to the solvent in the mitochondrial intermembrane space via a water chain. (B) As a reduced ubiquinol molecule binds to the site, the side chain of Glu-271 flips to form a hydrogen bond to the bound ubiquinone. (C) Now, the ISP, which is moving around the intermediate position by thermal motion is trapped at the b" position by a hydrogen bond to the bound ubiquinone. (D,E) Coupled to deprotonation, the first electron transfer occurs. Since the Rieske FeS cluster has a much higher redox potential (ca. +300 mV) than heme bl (ca. 0 mV), the first electron is favorably transferred to ISP. This yields ubisemiquinone, (F,G). After ubisemiquinone formation, the hydrogen bond to the His-161 of ISP is destabilized. The ISP moves to the c position, where the electron is transferred from the Rieske FeS cluster to heme c. Now unstable ubisemiquinone is left in the Qp pocket. The redox potential of the deprotonated ubisemiquinone is assumed to be several hundred millivolts. Now the electron transfer to the heme bl is a downhill reaction. (H) Coupled to the second electron transfer, the second proton is transferred to Glu-271 and subsequently to the mitochondrial intermembrane space. The fully oxidized ubiquinone is released to the membrane. 

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