Spontaneous spiral formation in two-dimensional oscillatory media

Petteri Kettunen, Takashi Amemiya, Takao Ohmori, and Tomohiko Yamaguchi

Phys. Rev. E 60, 1512-1515, 1999, DOI 10.1103/PhysRevE.60.1512.

Abstract: Computational studies of pattern formation in a modified Oregonator model of the Belousov-Zhabotinsky reaction is described. Initially inactive two-dimensional reaction media with an immobilized catalyst is connected to a reservoir of fresh reactants through a set of discrete points distributed randomly over the interphase surface. It is shown that the diffusion of reactants combined with oscillatory reaction kinetics can give rise to spontaneous spiral formation and phase waves.
PACS: 82.20.Mj, 47.54.+r, 82.20.Wt, 87.23.Cc


(a) p = 0.01

(b) p = 0.0625

(c) p = 0.075

(d) p = 0.15

Two-dimensional simulations of pattern formation with varying open diffusion site probabilities. Red indicates unexicited state of the catalyst and excited state is mapped to shades of blue. Elevated level of the propagator are shown as green (threshold 0.50). Variable p is the density of point diffusion sources distributed at random.

With increasing the density p, the patterns arising are: densely packed spirals (a); decreased number of spirals (b); mixture of circular phase waves and oscillating domains (c); bulk oscillations with no distinctive patterns (d).

Click on any image to play animation showing the dynamic evolution of those patterns.