Diffusion-driven stationary instability
= Diffusion-driven stationary instability
For reaction Jacobian $J=\begin{pmatrix}a&b\\c&d\end{pmatrix}$ with $\operatorname{tr}J<0$ and $\det J>0$, a Fourier mode evolves under $J-q^2\operatorname{diag}(D_u,D_v)$. Its determinant is $D_uD_vq^4-(D_va+D_ud)q^2+\det J$. A finite unstable band requires $D_va+D_ud>0$ and $(D_va+D_ud)^2>4D_uD_v\det J$, with an allowed domain mode in that band.