Pattern formation in coupled reaction-diffusion systems

A simplified coupled reaction-diffusion system is derived from a diffusive membrane coupling of two reaction-diffusion systems of activator-inhibitor type. It is shown that the dynamics of the original decoupled systems persists for weak coupling, while new coupled stationary patterns of alternated type emerge at a critical strength of coupling and become stable for strong coupling independently of the dynamics of the decoupled systems. The approach which we use here is singular perturbation techniques and complementarily numerical methods.