The Period Doubling bifurcation curve is defined by the following system
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this is exactly the system defining limit cycles but with one extra constraint G(u,T,a) = 0 where G(u,T,a) is defined as the solution component G of the system
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which is exactly the same system as was used to detect the Period Doubling bifurcation.
Instead of using this functional G both systems can be combined in one larger system
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The first method (using system (66) and (67)) is implemented in the curve definition file perioddoubling and the second (using system (68)) in perioddoubling2. For both methods the discretization is done using orthogonal collocation in the same way it was done for limit cycles.