Crossing bifurcations and unstable dimension variability.

  title={Crossing bifurcations and unstable dimension variability.},
  author={Kathleen T. Alligood and Evelyn Sander and J. A. Yorke},
  journal={Physical review letters},
  volume={96 24},
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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Ying-Cheng Lai

  • R. Davidchack
  • Athanasios Gavrielides, and Vassilios Kovanis…
  • 2000
2 Excerpts

Quantum Semiclass

  • M. Moller, B. Forsmann, W. Lange
  • Opt. 10, 1
  • 1998
2 Excerpts

Physica D (Amsterdam) 109

  • E. Kostelich, I. Kan, C. Grebogi, E. Ott, J. Yorke
  • 81
  • 1997
2 Excerpts


  • S. P. Dawson
  • Rev. Lett. 76, 4348
  • 1996

U(q) S(p) q p U(p) S(q) U(q) S(p) q p U(p) S(q) (a) (b) FIG. 6 (color online). For a crossing bifurcation, the twodimensional manifolds are either (a) untwisted or, (b) as in our example, twisted

  • B. Sandstede, Ph.D
  • J. Dyn. Differ. Equ. 5,
  • 1993
2 Excerpts

Physica D (Amsterdam) 58

  • F. J. Romeiras, C. Grebogi, E. Ott, W. P. Dayawansa
  • 165
  • 1992
2 Excerpts

William L

  • J. C. Sommerer
  • Ditto, Celso Grebogi, Edward Ott, and Mark L…
  • 1991
2 Excerpts

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