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

Aric Hagberg, Ehud Meron

Research output: Contribution to journalArticlepeer-review

118 Scopus citations


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 spatiotemporal processes have been observed recently in the ferrocyanide-iodate-sulfite reaction.

Original languageEnglish
Pages (from-to)477-484
Number of pages8
Issue number3
StatePublished - 1 Jan 1994
Externally publishedYes


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