The nonsmooth pitchfork bifurcation

The nonsmooth pitchfork bifurcation is uniquely defined as the moment of collision of three invariant curves. At the moment of bifurcation, the attractor is an SNA. Near this bifurcation point, in the region with just one attractor, a gradual smoothing process seems to transform the SNA to a smooth invariant curve. The moment of transition from SNA to an invariant curve is not well-defined numerically; see the computational results in Figure 21 and Figure 22.

Figure 8:

Nonsmooth pitchfork bifurcation with

= 0 and K = 0.9: (left) before the collision (

= 1.56765): attractors in blue and black, unstable invariant curves in green and red; (right) after the collision (

= 1.5675): SNA (black) and the unstable invariant curve not taking part in the bifurcation (green).

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, K)-plane

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Created by Hinke Osinga
Last modified: Wed May 17 16:11:06 2000