Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Experiment Videos

Crossing bifurcations and unstable dimension variability.

K T Alligood1, E Sander, J A Yorke

  • 1Mathematical Sciences, George Mason University, Fairfax, Virginia 22030, USA.

Physical Review Letters
|August 16, 2006
PubMed
Summary
This summary is machine-generated.

Related Concept Videos

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

Proportions of incommensurate, resonant, and chaotic orbits for torus maps.

Chaos (Woodbury, N.Y.)·2025
Same author

Why the United States Center for Medicare and Medicaid Services (CMS) should not extend reimbursement indications for carotid artery angioplasty/stenting.

International angiology : a journal of the International Union of Angiology·2012
Same author

[Data collection for quality assurance in neonatology: how do physicians compare to documentation specialists?].

Zeitschrift fur Geburtshilfe und Neonatologie·2006
Same author

Local low dimensionality of atmospheric dynamics.

Physical review letters·2001
Same author

Stagger-and-step method: detecting and computing chaotic saddles in higher dimensions.

Physical review letters·2001
Same author

Calcium channel blockers and the risk of cancer: a preclinical assessment.

Cardiovascular drugs and therapy·1998
Same journal

Erratum: Bacterial Turbulence at Compressible Fluid Interfaces [Phys. Rev. Lett. 136, 138301 (2026)].

Physical review letters·2026
Same journal

Unveiling Light-Quark Yukawa Flavor Structure via Dihadron Fragmentation at Lepton Colliders.

Physical review letters·2026
Same journal

Adaptable Route to Fast Coherent State Transport via Bang-Bang-Bang Protocols.

Physical review letters·2026
Same journal

Topological Transition and Emergence of Elasticity of Dislocation in Skyrmion Lattice: Beyond Kittel's Magnetic-Polar Analogy.

Physical review letters·2026
Same journal

Pound-Drever-Hall Method for Superconducting-Qubit Readout.

Physical review letters·2026
Same journal

Coupling a ^{73}Ge Nuclear Spin to an Electrostatically Defined Quantum Dot in Silicon.

Physical review letters·2026
See all related articles

Researchers identified a new type of crisis, a global bifurcation, in 3D chaotic systems. This phenomenon involves discontinuous changes in chaotic attractors and leads to unstable dimension variability.

Area of Science:

  • Dynamical Systems and Chaos Theory
  • Nonlinear Dynamics

Background:

  • A crisis is a global bifurcation where chaotic attractors change discontinuously or disappear with parameter variation.
  • Existing crisis bifurcations are understood in lower dimensions.

Purpose of the Study:

  • To describe a novel global bifurcation leading to a crisis in three-dimensional systems.
  • To investigate the characteristics and consequences of this new bifurcation.

Main Methods:

  • Analysis of a three-dimensional chaotic system exhibiting a crisis.
  • Identification of a bifurcation mechanism not involving tangency.
  • Derivation of a new scaling law for attractor density post-crisis.

Main Results:

  • A new class of crisis bifurcation in 3D systems is identified, distinct from tangency-based crises.

Related Experiment Videos

  • Evidence of unstable dimension variability is observed as a consequence of the crisis.
  • A novel scaling law is derived for the density of the newly formed attractor portion.

    • Conclusions:

    • This study reveals a previously undescribed crisis bifurcation in three-dimensional chaotic systems.
    • The findings highlight the role of higher dimensions in complex dynamical behaviors.
    • The derived scaling law offers new insights into attractor dynamics during crises.