Pattern formation in reaction–diffusion systems on evolving surfaces. (1st November 2020)

• Record Type: Journal Article
• Authors: Kim, Hyundong; Yun, Ana; Yoon, Sungha; Lee, Chaeyoung; Park, Jintae; Kim, Junseok
• Is Part Of: Computers & mathematics with applications. Volume 80:issue 9(2020)
• Page Start: 2019
• Page End: 2028
• Publication Date: 2020-11-01
• Subjects: Pattern formation -- Laplace–Beltrami operator -- Triangle surface mesh -- Reaction–diffusion system -- Evolving surface; Electronic data processing -- Periodicals; Mathematics -- Data processing -- Periodicals; 510.28541
• DOI: 10.1016/j.camwa.2020.08.026
• Languages: English
• ISSNs: 0898-1221

Abstract

Abstract: In this paper, we propose an explicit time-stepping scheme for the pattern formation in reaction–diffusion systems on evolving surfaces. The proposed numerical method is based on a simple discretization scheme of Laplace–Beltrami operator over triangulated surface. On the static and evolving domains, we perform various numerical experiments for effect of domain growth and pattern formations. The computational results demonstrate that our proposed method can simulate pattern formation in reaction–diffusion systems on evolving surfaces. The actual zebra skin pattern and computational results are compared. In the computational results, we can observe different pattern formations on the evolving surface with specific rotation speed. Highlights: An explicit time-stepping scheme is proposed for the pattern formation in the reaction–diffusion systems on evolving surfaces. The proposed numerical method is based on discretization of Laplace–Beltrami operator over triangulated surface. The proposed method can simulate the pattern formation in the reaction–diffusion systems on evolving surfaces.