This repository contains the code for the preprint
Diez A., Krause A. L., Maini P. K., Gaffney E. A., Seirin-Lee S., Turing pattern formation in reaction-cross-diffusion systems with a bilayer geometry, 2023
The goal of this article is to investigate the patterning conditions in general bilayer reaction-cross-diffusion systems either in a 1D-surface/2D-bulk situation or in the case of two coupled 1D layers. In these models, the different species are able to diffuse through an inteface via a linear transport law. Depending on the strength of the exchange rates between the two layers, different patterning scenarios are detailed in the article and confronted to numerical simulations which can be reproduced using the code provided in this repository.
1D-2D case:
1D-1D case:
The folder TuringSpace contains a numerical code to generate the Turing space of a large class of models with respect to arbitrary parameters as well as the various theoretical quantities derived in the article to study the bifurcation curves. Although this code has been written mostly for bilayer systems, it may be of independent interest to compute the Turing space of general monolayer reaction-cross-diffusion systems.
The folder BilayerRCD contains a custom Julia code for the simulation of a 2+3 components bilayer reaction-diffusion-chemotaxis system.
The folder supplementary_videos contains the supplementary videos described in the article.