Complex pattern formations by spatial varying parameters

Siqing Li*, Leevan LING

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

2 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)1327-1352
Number of pages26
JournalAdvances in Applied Mathematics and Mechanics
Issue number6
Early online dateSept 2020
Publication statusPublished - Dec 2020

Scopus Subject Areas

  • Mechanical Engineering
  • Applied Mathematics

User-Defined Keywords

  • Gierer-Meinhardt model
  • Meshless method
  • Pattern formation
  • Spatially varying parameter


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