Crossing bifurcations and unstable dimension variability.

@article{Alligood2006CrossingBA,
  title={Crossing bifurcations and unstable dimension variability.},
  author={Kathleen T. Alligood and Evelyn Sander and J. A. Yorke},
  journal={Physical review letters},
  year={2006},
  volume={96 24},
  pages={244103}
}
A crisis is a global bifurcation in which a chaotic attractor has a discontinuous change in size or suddenly disappears as a scalar parameter of the system is varied. In this Letter, we describe a global bifurcation in three dimensions which can result in a crisis. This bifurcation does not involve a tangency and cannot occur in maps of dimension smaller than 3. We present evidence of unstable dimension variability as a result of the crisis. We then derive a new scaling law describing the… CONTINUE READING

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