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Title: Mutually exclusive spiky pattern and segmentation modelled by the five-component meinhardt-gierer system
Authors: Winter, M
Wei, J
Keywords: Pattern Formation;Mutual Exclusion;Stability;Steady states
Issue Date: 2008
Publisher: Society for Industrial and Applied Mathematics
Citation: SIAM Journal on Applied Mathematics. 69 (1) 419-452
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.
Appears in Collections:Dept of Mathematics Research Papers
Mathematical Sciences

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