title: Crossing bifurcations and unstable dimension variability.
abstract: 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.
authors.affiliation: Mathematical Sciences, George Mason University, Fairfax, Virginia 22030, USA.
authors.forename: K T
authors.initials: KT
authors.lastname: Alligood
authors.forename: E
authors.initials: E
authors.lastname: Sander
authors.forename: J A
authors.initials: JA
authors.lastname: Yorke