Volume 12, Issue 6
Complex Pattern Formations by Spatial Varying Parameters

Siqing Li & Leevan Ling

Adv. Appl. Math. Mech., 12 (2020), pp. 1327-1352.

Published online: 2020-09

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  • 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.

  • Keywords

Gierer-Meinhardt model, pattern formation, meshless method, spatially varying parameter.

  • AMS Subject Headings

35K57, 65M70

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-12-1327, author = {Li , Siqing and Ling , Leevan}, title = {Complex Pattern Formations by Spatial Varying Parameters}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2020}, volume = {12}, number = {6}, pages = {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.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2018-0266}, url = {http://global-sci.org/intro/article_detail/aamm/18291.html} }
TY - JOUR T1 - Complex Pattern Formations by Spatial Varying Parameters AU - Li , Siqing AU - Ling , Leevan JO - Advances in Applied Mathematics and Mechanics VL - 6 SP - 1327 EP - 1352 PY - 2020 DA - 2020/09 SN - 12 DO - http://doi.org/10.4208/aamm.OA-2018-0266 UR - https://global-sci.org/intro/article_detail/aamm/18291.html KW - Gierer-Meinhardt model, pattern formation, meshless method, spatially varying parameter. AB -

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.

Siqing Li & Leevan Ling. (2020). Complex Pattern Formations by Spatial Varying Parameters. Advances in Applied Mathematics and Mechanics. 12 (6). 1327-1352. doi:10.4208/aamm.OA-2018-0266
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