Physical Sciences and Mathematics Commons^™

Instabilities And Patterns In Coupled Reaction-Diffusion Layers, Anne J. Catlla, Amelia Mcnamara, Chad M. Topaz

Chad M. Topaz

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 …