Mutually exclusive spiky pattern and segmentation modelled by the five-component meinhardt-gierer system

Abstract

We consider the five-component Meinhardt-Gierer model for mutually exclusive patterns and segmentation. We prove rigorous results on the existence and stability of mutually exclusive spikes which are located in different positions for the two activators. Sufficient conditions for existence and stability are derived, which depend in particular on the relative size of the various diffusion constants. Our main analytical methods are the Liapunov-Schmidt reduction and nonlocal eigenvalue problems. The analytical results are confirmed by numerical simulations.