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

Tracking controlled chaos: Theoretical foundations and applications.

Ira B. Schwartz1, Thomas W. Carr, Ioana Triandaf

  • 1Special Project in Nonlinear Science, Code 6700.3, Plasma Physics Division, Naval Research Laboratory, Washington, D.C. 20375.

Chaos (Woodbury, N.Y.)
|June 5, 2003
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

Delay induced swarm pattern bifurcations in mixed reality experiments.

Chaos (Woodbury, N.Y.)·2020
Same author

Torus bifurcations of large-scale swarms having range dependent communication delay.

Chaos (Woodbury, N.Y.)·2020
Same author

Unstable modes and bistability in delay-coupled swarms.

Physical review. E·2020
Same author

Quantitative and qualitative characterization of zigzag spatiotemporal chaos in a system of amplitude equations for nematic electroconvection.

Chaos (Woodbury, N.Y.)·2007
Same author

Approximating stable and unstable manifolds in experiments.

Physical review. E, Statistical, nonlinear, and soft matter physics·2003
Same author

Open-loop sustained chaos and control: a manifold approach.

Physical review. E, Statistical, nonlinear, and soft matter physics·2002
Same journal

Multiscale dynamics of special memristive ion channels in a neural circuit.

Chaos (Woodbury, N.Y.)·2026
Same journal

Symmetry-protected delay spectroscopy in oscillator networks.

Chaos (Woodbury, N.Y.)·2026
Same journal

Mesoscale community organization governs epidemic onset and spread in metapopulations.

Chaos (Woodbury, N.Y.)·2026
Same journal

Topological dependence of viral mutation spread in complex host-interaction networks.

Chaos (Woodbury, N.Y.)·2026
Same journal

Multifractal signatures of Hamiltonian chaos in Hyperion's rotational dynamics.

Chaos (Woodbury, N.Y.)·2026
Same journal

Exploring mechanisms for reversal of flow in tunicate hearts.

Chaos (Woodbury, N.Y.)·2026
See all related articles

This study introduces a theoretical framework for tracking unstable states in dynamical systems. This method enables experimental continuation of these states across various parameters, aiding the study of nonlinear dynamics.

Area of Science:

  • Nonlinear Dynamics
  • Control Theory
  • Experimental Physics

Background:

  • Tracking controlled states is crucial for studying unstable phenomena in chaotic and non-chaotic systems.
  • Unstable states are fundamental to understanding observed nonlinear dynamic phenomena.
  • Existing methods for analyzing unstable states are limited in scope and application.

Purpose of the Study:

  • To develop a theoretical foundation for tracking controlled unstable states.
  • To provide a constructive method for experimentally continuing unstable states as parameters change.
  • To demonstrate the broad applicability of tracking theory in dynamical system experiments.

Main Methods:

  • Developing a theoretical framework integrating dynamical systems and control theory.

Related Experiment Videos

  • Constructing an algorithmic approach to explicitly track curves of unstable states.
  • Applying the theory to various control techniques used in dynamical system experiments.

    • Main Results:

    • A constructive theory for tracking controlled states is presented.
    • The theory explicitly demonstrates how to track unstable states across parameter variations.
    • The framework is validated through numerical and physical experiments.

    Conclusions:

    • The developed theory provides a robust method for tracking unstable states in dynamical systems.
    • This approach enhances the experimental investigation of nonlinear dynamics.
    • The theory has wide-ranging applications in current dynamical system experiments.