Jove
Visualize
Contact Us

Related Experiment Videos

Imperfect homoclinic bifurcations.

P Glendinning1, J Abshagen, T Mullin

  • 1Department of Mathematics, UMIST, P.O. Box 88, Manchester M60 1QD, United Kingdom.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|October 3, 2001
PubMed
Summary

Experimental observations of an electronic circuit reveal complex bifurcation sequences. These dynamics are explained using imperfect global bifurcation theory, specifically imperfect homoclinic bifurcations, without needing a mathematical model.

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

On the buckling of an elastic holey column.

Proceedings. Mathematical, physical, and engineering sciences·2017
Same author

Buckling of a holey column.

Soft matter·2016
Same author

Granular segregation driven by particle interactions.

Physical review letters·2015
Same author

Towed body measurements of flow noise from a turbulent boundary layer under sea conditions.

The Journal of the Acoustical Society of America·2014
Same author

Hierarchy and polysynchrony in an adaptive network.

Physical review. E, Statistical, nonlinear, and soft matter physics·2014
Same author

Balancing a cylinder on a thin vertical layer of viscous fluid.

Physical review. E, Statistical, nonlinear, and soft matter physics·2013
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:

  • Nonlinear dynamics
  • Electronic circuits
  • Bifurcation theory

Background:

  • Electronic circuits can exhibit complex dynamical behaviors.
  • Bifurcation theory describes how system behavior changes qualitatively as parameters vary.
  • Global bifurcations, particularly homoclinic bifurcations, are crucial in understanding complex dynamics.

Purpose of the Study:

  • To analyze the complicated bifurcation sequences observed in an almost symmetric electronic circuit.
  • To explain these observed dynamics using the theory of imperfect global bifurcations.
  • To demonstrate the applicability of imperfect homoclinic bifurcations in understanding circuit dynamics without explicit modeling.

Main Methods:

  • Experimental observation of an electronic circuit's behavior.

Related Experiment Videos

  • Theoretical analysis using the framework of imperfect global bifurcations.
  • Comparison of experimental results with theoretical predictions of imperfect homoclinic bifurcations.

    • Main Results:

    • Observed complicated sequences of bifurcations in the electronic circuit.
    • Demonstrated that these dynamics can be understood through the lens of imperfect global bifurcations.
    • Showed that imperfect homoclinic bifurcations provide a sufficient explanation for the observed circuit dynamics.

    Conclusions:

    • The complex dynamics of the studied electronic circuit are well-described by imperfect global bifurcation theory.
    • Imperfect homoclinic bifurcations offer a powerful tool for analyzing and understanding nonlinear electronic systems.
    • Explicit mathematical modeling of the system is not always necessary to explain its complex dynamics.