Complex Patterns in Reaction-Diffusion Systems:
A Tale of Two Front Instabilities
Aric Hagberg 1,
and Ehud Meron 2
1 Program in Applied Mathematics, University of Arizona, Tucson, AZ 85721
2 Department of Mathematics and ACMS, University of Arizona, Tucson, AZ 85721
Published in Chaos, Volume 4, Number 3, September 1994
Two front instabilities in a reaction-diffusion system are shown to
lead to the formation of complex patterns. The first is an
instability to transverse modulations that drives the formation of
labyrinthine patterns. The second is a Nonequilibrium Ising-Bloch
(NIB) bifurcation that renders a stationary planar front unstable and
gives rise to a pair of counterpropagating fronts. Near the NIB
bifurcation the relation of the front velocity to curvature is highly
nonlinear and transitions between counterpropagating fronts become
feasible. Nonuniformly curved fronts may undergo local front
transitions that nucleate spiral-vortex pairs. These nucleation
events provide the ingredient needed to initiate spot splitting and
spiral turbulence. Similar spatio-temporal processes have been
observed recently in the ferrocyanide-iodate-sulfite reaction.
The entire document
The figures as:
Aric Hagberg <aric@lanl.gov>
Last modified: Wed Dec 17 11:16:49 MST 1997