Bifurcation fivefold

A fivefold bifurcation curve for y values in terms of the controller gain K... 

A call of pellet4etacurve(0.1,0.7,1,15,100,18,1,1) draws the following plot with fivefold bifurcation for the parameters as indicated in Figure 5.26. 

Fivefold bifurcating curve for ry, runtime 290 seconds Figure 5.26... 

Figure 5.27 shows another fivefold bifurcating /([Pg.320]

Another fivefold bifurcating curve for 77 runtime 340 seconds... 

For Figures 5.26 and 5.27 and the fivefold bifurcation case, each BVP takes around 1 second to solve in MATLAB on our 450 Mhz SunBlade 100. This nearly doubles the time of our average of 0.6 seconds per BVP solution for the earlier single second-order DE model which apparently can only model the no or the threefold bifurcation cases. 

It is important to understand that these measurements are difficult. Since 5 = 5, each successive bifurcation requires about a fivefold improvement in the experimenter s ability to measure the external control parameter. Also, experimental noise tends to blur the structure of high-period orbits, so it is hard to tell precisely when a bifurcation has occurred. In practice, one cannot measure more than about five period-doublings. Given these difficulties, the agreement between theory and experiment is impressive. 

This formal fivefold coordination, with two bifurcated H-bonds being about as strong as one normal H-bond, leads to a situation that the average coordination in water is larger than 4 as shown by spatial distribution functions, obtained both experimentally and computationally. A graph of the various most frequently occurring coordination numbers vs the fraction of O—O coordination 2.0-3.2 A is shown in Fig. 2.4. 

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