Stability analysis of Turing patterns generated by the Schnakenberg model.

We consider the following Schnakenberg model on the interval (-1,1): [formula see text] where D1 > 0, D2 > 0, B > 0. We rigorously show that the stability of symmetric N-peaked steady-states can be reduced to computing two matrices in terms of the diffusion coefficients D1, D2 and the number N of peaks. These matrices and their spectra are calculated explicitly and sharp conditions for linear stability are derived. The results are verified by some numerical simulations.