Jove
Visualize
Contact Us

Related Experiment Videos

Pattern formation in an N+Q component reaction-diffusion system.

John E. Pearson1, William J. Bruno

  • 1Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545.

Chaos (Woodbury, N.Y.)
|October 1, 1992
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 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
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

This study analyzes reaction-diffusion systems, revealing how immobile species enable pattern formation (Turing bifurcations). Substrate concentration impacts bifurcations but not the instability

Area of Science:

  • Chemical kinetics
  • Mathematical modeling
  • Pattern formation

Background:

  • Reaction-diffusion systems are crucial for understanding pattern formation in biological and chemical systems.
  • Turing bifurcations describe instabilities leading to spatial patterns from uniform states.
  • Existing models often simplify the role of immobile species in pattern initiation.

Purpose of the Study:

  • To analyze a general N+Q component reaction-diffusion system for pattern-forming instabilities (Turing bifurcations).
  • To investigate the influence of immobile species and substrate concentration on Turing instability.
  • To explore bifurcations in eigenspectra as substrate concentration varies.

Main Methods:

  • Analysis of a general N+Q component reaction-diffusion system.

Related Experiment Videos

  • Investigation of bifurcations from spatially uniform states and imposed gradients.
  • Examination of eigenspectra under varying substrate concentrations.

    • Main Results:

    • Immobile species, formed by substrate reactions, are essential for Turing instability.
    • Critical wave number and instability location are independent of substrate concentration.
    • A Hopf bifurcation occurs as total substrate concentration decreases.
    • Under identical diffusion rates, the mobile subsystem transitions from unstable focus to node at Turing bifurcation.

    Conclusions:

    • The proposed reaction-diffusion model provides a framework for understanding Turing pattern formation.
    • Immobile species play a critical role in initiating spatial instabilities.
    • Substrate concentration influences system dynamics, including Hopf bifurcations, but not the fundamental nature of the Turing instability.