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

Synchronization in oscillator networks with delayed coupling: a stability criterion.

Matthew G Earl1, Steven H Strogatz

  • 1Department of Theoretical and Applied Mechanics, 212 Kimball Hall, Cornell University, Ithaca, New York 14853-1503, USA. mge1@cornell.edu

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|April 12, 2003
PubMed
Summary

We found a stability criterion for synchronized identical phase oscillators with coupling delays. This stability condition works for any network structure where each oscillator receives signals from a uniform number of other oscillators.

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

Comparing the efficiency of forward and backward contact tracing.

Physical review. E·2023
Same author

A global synchronization theorem for oscillators on a random graph.

Chaos (Woodbury, N.Y.)·2022
Same author

Asymptotic Absorption-Time Distributions in Extinction-Prone Markov Processes.

Physical review letters·2022
Same author

Coupled metronomes on a moving platform with Coulomb friction.

Chaos (Woodbury, N.Y.)·2022
Same author

Modeling the Interplay Between Seasonal Flu Outcomes and Individual Vaccination Decisions.

Bulletin of mathematical biology·2022
Same author

How a minority can win: Unrepresentative outcomes in a simple model of voter turnout.

Physical review. E·2021

Area of Science:

  • Complex Systems
  • Nonlinear Dynamics
  • Network Science

Background:

  • Networks of coupled oscillators are fundamental to many natural and engineered systems.
  • Understanding the stability of synchronized states is crucial for predicting system behavior.
  • Delayed coupling introduces significant complexity to oscillator network dynamics.

Purpose of the Study:

  • To derive a general stability criterion for the synchronous state in networks of identical phase oscillators with delayed coupling.
  • To establish a condition applicable across diverse network topologies and dimensions.

Main Methods:

  • Mathematical analysis of coupled phase oscillator dynamics.
  • Derivation of a stability criterion based on network properties and coupling delay.

Related Experiment Videos

  • Application of the criterion to various network configurations.

    • Main Results:

    • A unified stability criterion for synchrony was derived.
    • The criterion is independent of network structure (regular, random, directed, undirected) and dimensionality.
    • The criterion depends on the uniform in-degree (k) of oscillators and the coupling delay.

    Conclusions:

    • A universal condition for the stability of synchronous states in delayed oscillator networks was established.
    • This finding simplifies the analysis of synchrony in complex networks with time delays.
    • The derived criterion provides a powerful tool for designing and analyzing synchronized systems.