Stability analysis for a stripe solution in the Gierer-Meinhardt system

Abstract

We consider the Gierer-Meinhardt system on a rectangle in two-dimensional space. This system is considered to generate some spiky pattern for a wide range of parameters. On a rectangle, this system also has a stripe solution, which is known to be unstable from numerical results. In this paper, we show the instability of the stripe pattern in a mathematically rigorous manner by using the SLEP method.