Rossler system period-doubling

The logistic map, referred to previously, is a now famous, but simple, quadratic function that displays the same period-doubling cascade into chaos exhibited by the Rossler system (and by quite a few experimental examples, as well). A map is an equation that gives an iterative rule for generating a sequence of points x, Xj, X3,... given an initial value Xq. The logistic map is given by... 

The Willamowski-RSssler rate equations yield both periodic and chaotic attractors as the system parameters are tuned [10,21]. One common scenario for the appearance of a chaotic attractor is a cascade of ppriod-doubling bifurcations. As can be seen in the bifurcation diagram in Figure 2, the Willamowski-Rossler reaction possesses such a bifurcation sequence the chaotic attractor is followed by a reverse cascade of period doublings leading, ultimately, to a steady state. 

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