Mutually Exclusive Spiky Pattern and Segmentation Modeled by the Five-Component Meinhardt--Gierer System

We consider the five-component Meinhardt-Gierer model for mutually exclusive patterns and segmentation which was proposed in [11]. 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. Key words. Pattern Formation, Mutual Exclusion, Stability, Steady states AMS subject classifications. Primary 35B35, 92C15; Secondary 35B40, 92D25

• Type: Journal
• Year: 2008
• Where: SIAMAM
• Authors: Juncheng Wei, Matthias Winter
• Keywords: Five-component Meinhardt-gierer Model, Mutually Exclusive, Nonlocal Eigenvalue Problems, SIAMAM 2008