= Turing threshold of the quadratic activator-inhibitor model
{c}
{title2=$0<b<1,\quad db>3+2\sqrt2$}
A mode with squared <wavenumber> $q$ in the <quadratic activator-inhibitor model> has negative trace $b-1-(1+d)q$ when $0<b<1$. Its determinant is $D(q)=dq^2+(1-db)q+b$. A positive minimum location and a negative minimum require $db>1$ and $(db-1)^2>4db$, equivalent to $db>3+2\sqrt2$. At onset, the double determinant root is $q_c=(1+\sqrt2)/d$. In a bounded domain an admissible nonzero spatial mode must additionally lie in the open negative-determinant band.
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