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Bistable reaction-diffusion systems can have robust zero-velocity fronts.

Jacques-Alexandre Sepulchre1, Valentin I. Krinsky

  • 1Institut Non-lineaire de Nice Sophia Antipolis, 1361 route des Lucioles, 06560 Valbonne, France.

Chaos (Woodbury, N.Y.)
|June 5, 2003
PubMed
Summary

Robust zero-velocity fronts are demonstrated in bistable reaction-diffusion systems. These stationary fronts persist even when diffusion coefficients vanish, offering stability unlike standard models.

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Area of Science:

  • Mathematical modeling
  • Chemical kinetics
  • Physics

Background:

  • Reaction-diffusion systems are crucial for modeling phenomena like pattern formation and chemical waves.
  • Bistable systems exhibit two stable states, leading to sharp interfaces or fronts.
  • Standard models often show front velocity is sensitive to parameter changes, with zero velocity occurring at isolated points.

Purpose of the Study:

  • To investigate the robustness of zero-velocity fronts in bistable reaction-diffusion systems.
  • To explore the behavior of these fronts in the singular limit where diffusion coefficients approach zero.
  • To contrast this robustness with the typical sensitivity of front velocity to parameter variations.

Main Methods:

  • Analysis of bistable reaction-diffusion equations.

Related Experiment Videos

  • Investigation in the singular limit of vanishing diffusion coefficients.
  • Examination of front velocity as a function of system parameters.

    • Main Results:

    • Zero-velocity fronts are shown to be robust in a specific class of bistable reaction-diffusion systems.
    • Stationary fronts persist despite variations in system parameters when a diffusion coefficient vanishes.
    • This robustness is a key difference from standard models where zero velocity is typically found only at isolated parameter values.

    Conclusions:

    • The singular limit provides a mechanism for robust stationary fronts in reaction-diffusion systems.
    • This finding has implications for understanding pattern stability and control in various scientific fields.
    • The robustness of zero-velocity fronts offers a new perspective on front dynamics in complex systems.