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This Demonstration shows how one can compute the bifurcation diagram for a nonlinear chemical system such as the three-variable autocatalator (see Details). Indeed, in order to obtain such a diagram, one has to locate the maxima of the time series for all values of the bifurcation parameter, ... , which can be readily done using Mathematica's built-in function ... . The Demonstration illustrates the dynamics of the concentrations ... , ... , and ... for various values of the bifurcation parameter ... . The time series option gives a plot of ... versus time and shows the loci of all maxima. Try the following values of ... : 0.1, 0.14, 0.15, 0.151, and 0.155 to observe period 1, 2, 4, 8, and 5 behaviors, respectively. For ... , chaotic behavior occurs. When ... is large enough, you can observe a reversed sequence leading back to period 1 behavior. These results are confirmed by the bifurcation diagram (a remerging Feigenbaum tree), first given in  and reproduced in the present Demonstration.
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