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Related Experiment Videos

Pattern formation in excitable media with concentration-dependent diffusivities.

Marc R Roussel1, Jichang Wang

  • 1Department of Chemistry and Biochemistry, University of Lethbridge, Lethbridge, Alberta, Canada T1K 3M4. roussel@uleth.ca

The Journal of Chemical Physics
|July 23, 2004
PubMed
Summary
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Pattern formation in excitable media transitions from self-replication to stationary spots as autocatalyst concentration influences diffusion. This shift, independent of relative diffusivities, depends on initial perturbation size and geometry.

Area of Science:

  • Chemical kinetics
  • Nonlinear dynamics
  • Mathematical modeling

Background:

  • Excitable media exhibit complex spatiotemporal patterns.
  • The Gray-Scott model is a common framework for studying pattern formation.
  • Concentration-dependent diffusion can significantly alter system dynamics.

Purpose of the Study:

  • Investigate pattern formation in a two-variable Gray-Scott model.
  • Analyze the effect of concentration-dependent diffusivities on pattern evolution.
  • Understand the transition from self-replicating patterns to stationary spots.

Main Methods:

  • Utilized a two-variable Gray-Scott model with concentration-dependent diffusion coefficients.
  • Simulated pattern formation under varying degrees of autocatalyst influence on diffusion.

Related Experiment Videos

  • Examined the impact of initial perturbation size and geometry on pattern outcomes.

    • Main Results:

    • Observed a transition from self-replicating behavior to stationary spots.
    • This transition occurred as the influence of autocatalyst concentration on diffusion increased.
    • Time-independent patterns showed an unusual dependence on initial perturbation characteristics.

    Conclusions:

    • Concentration-dependent diffusion is a key factor in controlling pattern formation in excitable media.
    • The transition to stationary spots is achievable without altering relative diffusivities.
    • Initial conditions play a critical role in determining the final pattern state.