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 - <p style="text-align: justify;">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.</p>