= Fast-inhibitor cubic activator growth rate
{title2=$\sigma(k)=-r-Dk^2+\rho k^2/(1+k^2)$}
For $u_t=Du_{xx}-u(u-r)(u-1)-\rho(v-u)$ and $0=v_{xx}-v+u$, a <Fourier mode> perturbation about zero has $v=u/(1+k^2)$ and <growth rate> $\sigma(k)=-r-Dk^2+\rho k^2/(1+k^2)$. If $\rho>D$, its maximum is $-r+(\sqrt\rho-\sqrt D)^2$ at $k^2=\sqrt{\rho/D}-1$; if $\rho\leq D$, its maximum is $-r$ at zero. Replacing $(u,v,r)$ by $(1-u,1-v,1-r)$ gives the corresponding criterion at the other homogeneous equilibrium.
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