Jove
Visualize
Contact Us

Related Experiment Videos

Robust dangerous border-collision bifurcations in piecewise smooth systems.

Munther A Hassouneh1, Eyad H Abed, Helena E Nusse

  • 1Department of Electrical and Computer Engineering and Institute for Systems Research, University of Maryland, College Park, MD 20742, USA.

Physical Review Letters
|March 5, 2004
PubMed
Summary

Novel border-collision bifurcations in dynamical systems can cause unbounded behavior. Researchers identified this fundamental phenomenon and developed a method to prevent these dangerous bifurcations in experiments.

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

Scaling properties of saddle-node bifurcations on fractal basin boundaries.

Physical review. E, Statistical, nonlinear, and soft matter physics·2004
See all related articles
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

Area of Science:

  • Dynamical Systems and Chaos Theory
  • Nonlinear Dynamics
  • Mathematical Physics

Background:

  • Systems described by piecewise smooth continuous maps with nondifferentiable surfaces exhibit complex behaviors.
  • Bifurcations are critical points where system dynamics change qualitatively.
  • Previous studies have not fully addressed bifurcations leading to unbounded behavior.

Purpose of the Study:

  • To identify and characterize novel bifurcations in piecewise smooth dynamical systems.
  • To understand the mechanism leading to unbounded behavior in these systems.
  • To propose a method for preventing dangerous border-collision bifurcations.

Main Methods:

  • Physical and computational experiments using piecewise smooth continuous maps.

Related Experiment Videos

  • Analysis of system orbits and fixed points around bifurcation values.
  • Development and testing of a preventative method for bifurcations.

    • Main Results:

    • Discovery of a new class of border-collision bifurcations.
    • Demonstration that these bifurcations typically lead to unbounded orbits.
    • Confirmation of the fundamental and robust nature of these bifurcations.
    • Presentation of a successful method to prevent these dangerous bifurcations.

    Conclusions:

    • Border-collision bifurcations in piecewise smooth systems are a significant source of unpredictable dynamics.
    • The identified bifurcations are robust and can occur in various experimental settings, including electronic circuits.
    • The proposed method offers a practical solution for controlling and avoiding unbounded behavior in such systems.