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

Pattern dynamics in a checkerboard map.

N J Balmforth1, E A Spiegel

  • 1Departments of Mathematics and Earth and Ocean Science, University of British Columbia, Vancouver, British Columbia V6T 1Z2, Canada.

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

Rapidly rotating Rayleigh-Bénard convection with a tilted axis.

Physical review. E·2019
Same author

Generation of Large-Scale Winds in Horizontally Anisotropic Convection.

Physical review letters·2015
Same author

The speed of an inclined ruck.

Proceedings. Mathematical, physical, and engineering sciences·2015
Same author

[Principles and applications of stereoencephalotomy].

Acta neurochirurgica·2014
Same author

Picrotoxin-Barbiturates Antagonism in Decorticated Animals.

The Yale journal of biology and medicine·2011
Same author

Anticonvulsant effect of pregnenolone.

Federation proceedings·2010
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
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
See all related articles

Singular perturbation theory simplifies complex differential equation solutions. Checkerboard-style maps predict pulse sequences and spacings, even with chaotic systems and coexisting pulse types.

Area of Science:

  • Mathematics
  • Applied Mathematics
  • Dynamical Systems

Background:

  • Differential equations frequently exhibit solutions as trains of coherent structures like pulses and antipulses.
  • Singular perturbation theory offers a method to derive pattern maps predicting pulse spacings in such systems.

Purpose of the Study:

  • To apply singular perturbation theory to systems with coexisting distinct pulse types.
  • To simplify the description of complex pulse successions and spacings, particularly in chaotic scenarios.

Main Methods:

  • Application of singular perturbation theory to derive pattern maps.
  • Development of checkerboard-style maps to represent pulse sequences and spacings.
  • Analysis of systems with two distinct coexisting pulse or antipulse types.

Related Experiment Videos

Main Results:

  • Direct application of the method yields multivalued maps for systems with multiple pulse types.
  • Checkerboard-style maps provide a simplified, causal description of pulse successions and spacings.
  • The method effectively handles chaotic sequences of pulse types.

Conclusions:

  • Checkerboard-style maps offer a more intuitive and manageable approach to analyzing complex pulse dynamics.
  • This method enhances the understanding of pattern formation in differential equations with diverse coherent structures.
  • The findings are applicable to various scientific fields relying on the analysis of differential equations.