Brusselator trapping region
= Brusselator trapping region
{c}
For the spatially homogeneous Brusselator with parameters $r,s>0$, set $\alpha=r/(1+s)$. The quadrilateral
$$
\alpha\leq x,\qquad
0\leq y\leq\frac s\alpha,\qquad
x+y\leq r+\frac s\alpha
$$
is a <trapping region>. The four inward-pointing tests use $\dot x\geq0$ on $x=\alpha$, $\dot y\geq0$ on $y=0$, $\dot y\leq0$ on $y=s/\alpha$, and $\dot x+\dot y=r-x\leq0$ on the sloping edge.