Abstract
Patterns containing multiple length scales arise in a variety of
natural systems such as lateral veins in leaves, fingerprints, wrinkled
skin, and dendritic crystals. Here we observe period-doubling and
bursting instabilities in the spatial extent of wave propagation in
a gel-filled capillary tube open at one end and containing the Belousov–Zhabotinsky
(BZ) reaction–diffusion system. We analyze the relationship
between the multiple propagation distances of pulse waves and the
local kinetics of the reaction–diffusion system. Simulations
with a five-variable Oregonator model qualitatively mimic the multiple
length scale patterns of pulse propagation observed in our experiments,
suggesting that the study of these phenomena in reaction–diffusion
systems may be helpful in understanding complex multiple length scale
dynamical behaviors in nature.