Instabilities and patterns in coupled reaction-diffusion layers
Published by the American Physical Society URL: http://link.aps.org/doi/10.1103/PhysRevE.85.026215 DOI: 10.1103/PhysRevE.85.026215 PACS: 05.45.-a, 82.40.Bj
We study instabilities and pattern formation in reaction-diffusion layers that are diffusively coupled. For two-layer systems of identical two-component reactions, we analyze the stability of homogeneous steady states by exploiting the block symmetric structure of the linear problem. There are eight possible primary bifurcation scenarios, including a Turing-Turing bifurcation that involves two disparate length scales whose ratio may be tuned via the interlayer coupling. For systems of n-component layers and nonidentical layers, the linear problem’s block form allows approximate decomposition into lower-dimensional linear problems if the coupling is sufficiently weak. As an example, we apply these results to a two-layer Brusselator system. The competing length scales engineered within the linear problem are readily apparent in numerical simulations of the full system. Selecting a 2:1 length-scale ratio produces an unusual steady square pattern.
Anne J. Catlla, Amelia McNamara, and Chad M. Topaz. "Instabilities and patterns in coupled reaction-diffusion layers" Physical Review E 85.2 (2012): 026215-1-026215-11.
Available at: http://works.bepress.com/chad_topaz/18