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Article
Instabilities and patterns in coupled reaction-diffusion layers
Physical Review E (2012)
  • Anne J Catlla
  • Amelia McNamara, Macalester College
  • Chad M Topaz, Macalester College
Abstract

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.

Publication Date
2012
Publisher Statement
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
Citation Information
Anne J Catlla, Amelia McNamara and Chad M Topaz. "Instabilities and patterns in coupled reaction-diffusion layers" Physical Review E Vol. 85 Iss. 2 (2012)
Available at: http://works.bepress.com/chad_topaz/18/