Instabilities and Patterns in Coupled Reaction-Diffusion Layers

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 inter-layer coupling. For systems of $n$-component layers and non-identical 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 $\sqrt{2}$:1 length scale ratio produces an unusual steady square pattern.

13 pages, 5 figures, accepted for publication in Phys. Rev. E

References in corpus (2)

• Turing patterns in network-organized activator-inhibitor systems
• Three-wave interactions and spatio-temporal chaos

Cited by in corpus (3)

• Spatiotemporal chaos and quasipatterns in coupled reaction-diffusion systems
• Stability analysis for a new model of multispecies convection-diffusion-reaction in poroelastic tissue
• Modern Perspectives on Near-Equilibrium Analysis of Turing Systems