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

A simple time-delay feedback anticontrol method made rigorous.

Tianshou Zhou1, Guanrong Chen, Qigui Yang

  • 1Department of Mathematical Sciences, Tsinghua University, Beijing 100084, People's Republic of China. zhou@polaris.s.kanazawa-u.ac.jp

Chaos (Woodbury, N.Y.)
|September 28, 2004
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

Influence of Rhenium Content on Vacancy-Type Defect Distribution in Mo-Re Alloys Under Room-Temperature Irradiation.

Materials (Basel, Switzerland)·2026
Same author

Laplacian spectrum constrains collective performance enhancement.

Physical review. E·2026
Same author

Coexistence of many positive invariant sets in several classes of dynamical systems.

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

Fuzzy reinforcement learning synchronization of stochastic dynamic networks: An adaptive event-triggered strategy.

Neural networks : the official journal of the International Neural Network Society·2026
Same author

Bipartite Containment of Second-Order Multiagent Systems With Compound Noise Under Fixed or Markovian Switching Signed Topology.

IEEE transactions on cybernetics·2026
Same author

A review of recent advances in generative artificial intelligence models for biomolecular sciences.

Acta pharmaceutica Sinica. B·2026
Same journal

Exploring mechanisms for reversal of flow in tunicate hearts.

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

State estimation in spatiotemporal chaos via low-rank StatFEM.

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

Universal response functions in driven dissipative tunneling dynamics.

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

A network-based approach to characterize the dynamics of the coupling field of thermoacoustic oscillators in annular geometry.

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

Data-driven soliton manifold approximations for dark and bright waves: Some prototypical 1D case examples.

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

Gap junction architecture and synchronization clusters in the thalamic reticular nuclei.

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

This study introduces a rigorous mathematical method to induce chaos in nonchaotic systems using time-delay feedback. The findings demonstrate how to control systems towards chaotic behavior, verified by simulations.

Area of Science:

  • * Control Theory
  • * Nonlinear Dynamics
  • * Chaos Theory

Background:

  • * Continuous-time autonomous systems often exhibit complex dynamics.
  • * Inducing and rigorously defining chaos is a significant challenge in nonlinear dynamics.
  • * Time-delay feedback is a known method for controlling system behavior.

Purpose of the Study:

  • * To develop a rigorous mathematical framework for chaotification using time-delay feedback.
  • * To establish conditions for transforming nonchaotic systems into chaotic ones.
  • * To ensure the generated chaos adheres to the Li-Yorke definition via the Marotto theorem.

Main Methods:

  • * Derivation of mathematical conditions for chaotification.
  • * Application of time-delay feedback control.

Related Experiment Videos

  • * Utilization of the Marotto theorem to confirm Li-Yorke chaos.
  • * Numerical simulations for validation.

    • Main Results:

    • * A rigorous method for chaotification via time-delay feedback is established.
    • * Mathematical conditions are derived to control systems into a chaotic state.
    • * The generated chaos is proven to be Li-Yorke chaotic using the Marotto theorem.
    • * Numerical simulations confirm the theoretical predictions.

    Conclusions:

    • * Time-delay feedback offers an effective and rigorous method for inducing chaos.
    • * The study provides a theoretical basis and practical validation for controlling chaos.
    • * This work contributes to a deeper understanding of chaos generation in dynamical systems.