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The structure of bifurcations in the (, K)-plane

Here, we restrict to the section = 0. The bifurcation structure in this section is shown in Figure 6.

Figure 6:	A cross-section at = 0 of the second overlap over a 200 X 200 grid. A point in the white region corresponds to two invariant curves, one is stable and the other is unstable. The region in which the stable curve is extremely wrinkled (large phase sensitivity) is marked as well.

The multistable regions only exist for large K. Figure 7 shows the bifurcations that happen as K decreases.

Figure 7:	Sketches of the bifurcations along the line in the second overlapping region as K decreases from 0.8 to 0. The bifurcation structure of Figure 3 (right) for K = 0.8 transforms into one like Figure 3 (left) by ``absorbing'' pairs of saddle-node bifurcations in the second pitchfork bifurcation.

If K is large enough, the saddle-node and pitchfork bifurcations can become nonsmooth.

	The nonsmooth pitchfork bifurcation
	The nonsmooth saddle-node bifurcation
	A nonsmooth bifurcation point of codimension two

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Created by Hinke Osinga
Last modified: Wed May 17 16:10:59 2000