Bifurcation tertiary

From the first transition state (TSl, Fig. 1), the reaction path leads to the tetrahedral intermediate 1 (INTI). In the latter, the proton transfer from methanol to the tertiary amine function is completed (from 1.183 to 1.059 A), and the negative charge at the former carbonyl oxygen atom reaches its maximum. This charge is compensated by a further shortening of the bifurcated hydrogen bonds to 2.040 A (-0.103 A) and 1.765 A (-0.096 A) (Fig. 1). The thiourea moiety thus forms an oxyanion hole similar to the amide groups of the serine protease backbone [41]. 

All transitions associated with secondary bifurcations have now been completely classified. Moreover, several examples of tertiary or even quaternary branchings are known both for steady-state and for time-periodic solutions (see, e.g., Iooss6 and Erneux and Reiss7 for some recent results). 

Now that it is substantiated that the [2Fe 2S] domain of the Rieske iron-sulfur protein is not static but moves between domains of cytochrome-c, and cytochrome-/ subunits, and that it is likely that such movement may provide a novel mechanism to allow catalysis of all the reactions involved in the oxidation of hydroquinone at the Qo site and the subsequent bifurcated pathway of electron transfer. It has been found that during the movement, the mobile [2Fe 2S] domain retains essentially the same tertiary structure, and the anchoring N-terminal tail of the R-ISP molecule remains in the same fixed position. The movement occurs through an extension of a helical segment in the short linking span. 

We have exhibited periodic and quasi-periodic behavior on the upper branch of the neutral stability curves. In this section, we consider the Boussinesq type model [1] near the lower branch of the neutral stability curves and exhibit a tertiary bifurcation to periodic behavior on this branch. 

We show that a tertiary bifurcation to stable time-periodic solution can be observed when G is progressively decreased. 

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