The Forcing Diagram:

The forcing diagram indicates how the ordering of the creation of orbits is dependent upon prior orbits. Here we plot the creation of period 3 (red) and period 4 (green) orbits for the classical logistic map. The control parameter is varied from 3.8 to 4.0 as the animation progresses (y axis) and the location of the orbits is indicated by their bifurcation position (x axis).

These are pairs of points created together at saddle node bifurcations. If we were to reverse the control parameter, it is obvious that the higher orbits (the inner pairs) must be destroyed before the lower orbits (outer pairs) can be annihilated. It is these topological considerations which determine the order of orbit creation/annihilation in one-dimensional maps.

Click here for the C++ code used to generate the orbit values seen above.

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The Nonlinear Dynamics Group at Drexel University.

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