Trapping triangle for a saturating monostable invasion front ($a^{\prime }=b,b^{\prime }=-cb-a({\eta }^2-a^2)/(1+a^2)$)

For $c>2\eta$, the triangle $0\le a\le \eta$, $-\eta a\le b\le 0$ traps the unstable branch leaving the saddle $(\eta ,0)$ toward lower population. On its top edge $b^{\prime }<0$. On the sloping edge, $(b+\eta a{)}^{\prime }=\eta (c-\eta )a-a({\eta }^2-a^2)/(1+a^2)>0$, so that edge is also inward. The right edge has $a^{\prime }=b\le 0$. Monotonicity of $a$ inside the compact region leaves only $(0,0)$ as the forward limit. This proves a nonnegative monotone travelling front. For $0<c<2\eta$, the target equilibrium is a focus, so any approaching nonconstant trajectory crosses into negative population and cannot be a physical front.