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

Analysis of a parametrically driven pendulum.

R Kobes1, J Liu, S Peles

  • 1Department of Physics, University of Winnipeg, Winnipeg, Manitoba, Canada R3B 2E9. randy@theory.uwinnipeg.ca

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|April 20, 2001
PubMed
Summary

This study explores a nonlinear mechanical system, revealing distinct regions of periodic, quasiperiodic, and chaotic behaviors using bifurcation diagrams. Symbolic dynamics analysis proves effective for understanding ordinary differential equations.

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

Fatigue reduction by sequential stimulation of multiple motor points in a muscle.

Clinical orthopaedics and related research·1995
Same author

Prospective, auto-controlled study on reinsemination of failed-fertilized oocytes by intracytoplasmic sperm injection.

Fertility and sterility·1995
Same author

Fluidity of the lipid domain of cell wall from Mycobacterium chelonae.

Proceedings of the National Academy of Sciences of the United States of America·1995
Same author

Effect of oleanolic acid on hepatic toxicant-activating and detoxifying systems in mice.

The Journal of pharmacology and experimental therapeutics·1995
Same author

Denaturant unfolding of the ferric enterobactin receptor and ligand-induced stabilization studied by site-directed spin labeling.

Biochemistry·1995
Same author

Identification of an essential cysteinyl residue in the ArsC arsenate reductase of plasmid R773.

Biochemistry·1995

Area of Science:

  • Nonlinear Dynamics
  • Mechanical Systems Analysis
  • Chaos Theory

Background:

  • Periodically driven nonlinear mechanical systems exhibit complex behaviors.
  • Understanding the parameter space of such systems is crucial for predicting their dynamics.

Purpose of the Study:

  • To investigate the behavior of a periodically driven nonlinear mechanical system.
  • To identify regions of periodic, quasiperiodic, and chaotic motion.
  • To assess the applicability of symbolic dynamics to ordinary differential equations.

Main Methods:

  • Construction and analysis of bifurcation diagrams.
  • Application of symbolic dynamics analysis.
  • Study of two-dimensional maps and their relation to ordinary differential equations.

Related Experiment Videos

Main Results:

  • Bifurcation diagrams successfully mapped regions of quasiperiodic, periodic, and chaotic behavior.
  • Symbolic dynamics of two-dimensional maps were effectively applied to the studied system.
  • Global knowledge of the ordinary differential equations was gained through symbolic analysis.

Conclusions:

  • The study successfully characterized the dynamics of the nonlinear mechanical system.
  • Symbolic dynamics provides a powerful tool for analyzing ordinary differential equations.
  • This approach offers a method for gaining global insights into complex dynamical systems.