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 dynamical systems approach to spiral wave dynamics.

Dwight Barkley1, Ioannis G. Kevrekidis

  • 1Department of Mathematics and Center for Nonlinear Dynamics, University of Texas, Austin, Texas 78712Laboratoire de Physique, Ecole Normale Superieure de Lyon, 46 Allee d'Italie, 69364 Lyon, FranceDepartment of Chemical Engineering, Princeton University, Princeton, New Jersey 08544.

Chaos (Woodbury, N.Y.)
|September 1, 1994
PubMed
Summary

A simple system of five nonlinear ordinary differential equations can replicate complex spiral wave dynamics in excitable media. This model offers insights into pattern formation in biological and chemical systems.

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

Phase Transition to Turbulence via Moving Fronts.

Physical review letters·2024
Same author

Extreme events in transitional turbulence.

Philosophical transactions. Series A, Mathematical, physical, and engineering sciences·2022
Same author

A fluid mechanic's analysis of the teacup singularity.

Proceedings. Mathematical, physical, and engineering sciences·2020
Same author

The rise of fully turbulent flow.

Nature·2015
Same author

Prediction of frequencies in thermosolutal convection from mean flows.

Physical review. E, Statistical, nonlinear, and soft matter physics·2015
Same author

Asymptotic dynamics of reflecting spiral waves.

Physical review. E, Statistical, nonlinear, and soft matter physics·2015

Area of Science:

  • Computational Biology
  • Nonlinear Dynamics
  • Mathematical Modeling

Background:

  • Spiral waves are complex spatiotemporal patterns observed in various excitable media.
  • Understanding the fundamental mechanisms governing spiral wave dynamics is crucial in fields like biology and chemistry.

Purpose of the Study:

  • To present a simplified mathematical model capable of reproducing key features of spiral waves.
  • To demonstrate the utility of nonlinear ordinary differential equations in modeling complex phenomena.

Main Methods:

  • Development of a system of five nonlinear ordinary differential equations.
  • Simulation and analysis of the model's behavior in a two-dimensional excitable medium.

Main Results:

Related Experiment Videos

  • The proposed system successfully reproduced diverse dynamical behaviors characteristic of spiral waves.
  • The model captured essential features such as wave propagation, meandering, and interaction.

Conclusions:

  • A concise five-equation system can effectively simulate complex spiral wave dynamics.
  • This simplified model serves as a valuable tool for studying pattern formation in excitable systems.