Abstract We consider the Gierer-Meinhardt system with small inhibitor diffusivity and very small activator diffusivity on a compact two-dimensional Riemannian manifold without boundary. We study steady state solutions which are far from spatial homogeneity. We construct two different spike clusters, each consisting of two spikes, which both approach the same nondegenerate local maximum point of the Gaussian curvature. We show that one of these spike clusters is stable, the other one is unstable.

中文翻译：

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紧凑二维黎曼流形上的稳定尖峰簇

摘要 我们在无边界的紧凑二维黎曼流形上考虑具有小抑制剂扩散系数和非常小的活化剂扩散系数的 Gierer-Meinhardt 系统。我们研究远离空间均匀性的稳态解。我们构建了两个不同的尖峰簇，每个尖峰由两个尖峰组成，它们都接近高斯曲率的相同非退化局部最大值点。我们表明这些尖峰簇之一是稳定的，另一个是不稳定的。