Pattern formation in reaction–diffusion systems on evolving surfaces

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.