title: Square Turing patterns in reaction-diffusion systems with coupled layers.
abstract: Square Turing patterns are usually unstable in reaction-diffusion systems and are rarely observed in corresponding experiments and simulations. We report here an example of spontaneous formation of square Turing patterns with the Lengyel-Epstein model of two coupled layers. The squares are found to be a result of the resonance between two supercritical Turing modes with an appropriate ratio. Besides, the spatiotemporal resonance of Turing modes resembles to the mode-locking phenomenon. Analysis of the general amplitude equations for square patterns reveals that the fixed point corresponding to square Turing patterns is stationary when the parameters adopt appropriate values.
authors.affiliation: State Key Laboratory for Mesoscopic Physics and School of Physics, Peking University, Beijing 100871, China.
authors.forename: Jing
authors.initials: J
authors.lastname: Li
authors.affiliation: State Key Laboratory for Mesoscopic Physics and School of Physics, Peking University, Beijing 100871, China.
authors.forename: Hongli
authors.initials: H
authors.lastname: Wang
authors.affiliation: State Key Laboratory for Mesoscopic Physics and School of Physics, Peking University, Beijing 100871, China.
authors.forename: Qi
authors.initials: Q
authors.lastname: Ouyang