The Period Doubling bifurcation curve is defined by the following system
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(64) |
this is exactly the system defining limit cycles but with one extra constraint
where
is defined as the solution component
of the system
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(65) |
which is exactly the same system as was used to detect the Period Doubling bifurcation.
Instead of using this functional
both systems can be combined in one larger system
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(66) |
The first method (using system (64) and (65)) is implemented in the curve definition file perioddoubling.
The other method is implemented in perioddoubling2. We will not use it further and it should not be confused with the
continuation of the period doubled curve that branches off in a PD point on a limit cycle curve.