title: Stable squares and other oscillatory turing patterns in a reaction-diffusion model.
abstract: We study the Brusselator reaction-diffusion model under conditions where the Hopf mode is supercritical and the Turing band is subcritical. Oscillating Turing patterns arise in the system when bulk oscillations lose their stability to spatial perturbations. Spatially uniform external periodic forcing can generate oscillating Turing patterns when both the Turing and Hopf modes are subcritical in the autonomous system. Most of the symmetric patterns show period doubling in both space and time. Patterns observed include squares, rhombi, stripes, and hexagons.
authors.affiliation: Department of Chemistry and Volen Center for Complex Systems, MS 015, Brandeis University, Waltham, Massachusetts 02454-9110, USA.
authors.forename: Lingfa
authors.initials: L
authors.lastname: Yang
authors.forename: Anatol M
authors.initials: AM
authors.lastname: Zhabotinsky
authors.forename: Irving R
authors.initials: IR
authors.lastname: Epstein