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

Control of multidimensional integrable Hamiltonian systems.

C W Kulp1, E R Tracy

  • 1Department of Physics and Astronomy, Eastern Kentucky University, Richmond, Kentucky 40475, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|October 26, 2005
PubMed
Summary

We investigated the controllability of a four-dimensional integrable Hamiltonian system. Applying small control coupling results in a Takens-Bogdanov bifurcation, increasing noise sensitivity and requiring noise threshold analysis.

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

Using forbidden ordinal patterns to detect determinism in irregularly sampled time series.

Chaos (Woodbury, N.Y.)·2016
Same author

Discriminating chaotic and stochastic dynamics through the permutation spectrum test.

Chaos (Woodbury, N.Y.)·2014
Same author

Detecting chaos in irregularly sampled time series.

Chaos (Woodbury, N.Y.)·2013
Same author

Noise-stabilized random attractor.

Physical review. E, Statistical, nonlinear, and soft matter physics·2006
Same author

Control of integrable Hamiltonian systems and degenerate bifurcations.

Physical review. E, Statistical, nonlinear, and soft matter physics·2004

Area of Science:

  • Nonlinear Dynamics
  • Control Theory
  • Mathematical Physics

Background:

  • Integrable Hamiltonian systems are fundamental in physics.
  • Low-mode truncation of the nonlinear Schrödinger equation yields a four-dimensional system.
  • Controllability analysis is crucial for understanding system behavior under external influence.

Purpose of the Study:

  • To analyze the controllability of a specific four-dimensional integrable Hamiltonian system.
  • To investigate the occurrence and implications of bifurcations under control.
  • To determine the noise sensitivity and establish a noise threshold for the controlled system.

Main Methods:

  • Analysis of a four-dimensional integrable Hamiltonian system derived from the nonlinear Schrödinger equation.

Related Experiment Videos

  • Application of control theory to target specific system dynamics.
  • Identification of Takens-Bogdanov bifurcations in the small control coupling limit.
  • Implementation of a noise threshold extraction algorithm.

    • Main Results:

    • A Takens-Bogdanov bifurcation is shown to occur at the control target for small control coupling.
    • This bifurcation generically arises when applying dissipative control to integrable Hamiltonian systems.
    • The Takens-Bogdanov bifurcation leads to extreme sensitivity to noise.
    • A subcritical noise threshold for the four-dimensional system was successfully extracted.

    Conclusions:

    • The study confirms the generic occurrence of Takens-Bogdanov bifurcations in controlled integrable Hamiltonian systems.
    • The identified noise sensitivity necessitates careful consideration of noise thresholds in control applications.
    • The implemented algorithm provides a method for quantifying noise resilience in such systems.