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Complex patterns in reaction-diffusion systems: A tale of two front instabilities.

Aric Hagberg1, Ehud Meron

  • 1Program in Applied Mathematics, University of Arizona, Tucson, Arizona 85721Arizona Center for Mathematical Sciences, Department of Mathematics, University of Arizona, Tucson, Arizona 85721.

Chaos (Woodbury, N.Y.)
|September 1, 1994
PubMed
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Complex patterns emerge from two front instabilities in reaction-diffusion systems. These instabilities generate labyrinthine patterns and counterpropagating fronts, leading to spiral turbulence, as seen in chemical reactions.

Area of Science:

  • Chemical kinetics
  • Pattern formation
  • Nonlinear dynamics

Background:

  • Reaction-diffusion systems exhibit complex spatiotemporal behaviors.
  • Front instabilities are key mechanisms driving pattern formation.

Purpose of the Study:

  • Investigate two front instabilities in reaction-diffusion systems.
  • Understand the mechanisms leading to complex pattern formation, including spiral turbulence.

Main Methods:

  • Analysis of front instabilities in a reaction-diffusion model.
  • Mathematical modeling of transverse modulations and nonequilibrium Ising-Bloch bifurcation.
  • Investigation of front velocity-curvature relations and front transitions.

Main Results:

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  • Transverse modulations lead to labyrinthine patterns.
  • Nonequilibrium Ising-Bloch bifurcation creates counterpropagating fronts.
  • Nonlinear front dynamics enable spiral-vortex pair nucleation, initiating spot splitting and spiral turbulence.

    • Conclusions:

    • Two distinct front instabilities drive complex pattern formation in reaction-diffusion systems.
    • The observed phenomena are relevant to experimental systems like the ferrocyanide-iodate-sulfite reaction.