Volgenau School of Engineering
George Mason University
George Mason University Mason
George Mason University

Three-dimensional crisis: crossing bifurcations and unstable dimension variablility


Publication Details MORE LESS

  • Published Date: June 3, 2006
  • Volume/Issue: 96
  • Publisher: Physical Review Letters


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 density of the new portion of the attractor formed in the crisis. We illustrate this new type of bifurcation with a specific example of a three-dimensional chaotic attractor undergoing a crisis.

Other Contributors

E. Sander and J. Yorke