Aric Hagberg

Development of Standing-Wave Labyrinthine Patterns

Arik Yochelis, Aric Hagberg, Ehud Meron, Anna L. Lin, and Harry L. Swinney,

SIADS, 1(2):236-247, 2002.

LA-UR-01-5306 http://math.lanl.gov/~hagberg/Publications/yochelis-2002-development.shtml

Abstract

Experiments on a quasi-two-dimensional Belousov--Zhabotinsky (BZ) reaction-diffusion system, periodically forced at approximately twice its natural frequency, exhibit resonant labyrinthine patterns that develop through two distinct mechanisms. In both cases, large amplitude labyrinthine patterns form that consist of interpenetrating fingers of frequency-locked regions differing in phase by $\pi$. Analysis of a forced complex Ginzburg--Landau equation captures both mechanisms observed for the formation of the labyrinths in the BZ experiments: a transverse instability of front structures and a nucleation of stripes from unlocked oscillations. The labyrinths are found in the experiments and in the model at a similar location in the forcing amplitude and frequency parameter plane.