Year: 2020
Author: Siqing Li, Leevan Ling
Advances in Applied Mathematics and Mechanics, Vol. 12 (2020), Iss. 6 : pp. 1327–1352
Abstract
Pattern formations by Gierer-Meinhardt (GM) activator-inhibitor model are considered in this paper. By linear analysis, critical value of bifurcation parameter can be evaluated to ensure Turing instability. Numerical simulations are tested by using second order semi-implicit backward difference methods for time discretization and the meshless Kansa method for spatially discretization. We numerically show the convergence of our algorithm. Pattern transitions in irregular domains are shown. We also provide various parameter settings on some irregular domains for different patterns appeared in nature. To further simulate patterns in reality, we construct different kinds of animal type domains and obtain desired patterns by applying proposed parameter settings.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.OA-2018-0266
Advances in Applied Mathematics and Mechanics, Vol. 12 (2020), Iss. 6 : pp. 1327–1352
Published online: 2020-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 26
Keywords: Gierer-Meinhardt model pattern formation meshless method spatially varying parameter.
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