= Trapping triangle for a saturating monostable invasion front
{title2=$a'=b,\quad b'=-cb-a(\eta^2-a^2)/(1+a^2)$}
For $c>2\eta$, the triangle $0\leq a\leq\eta$, $-\eta a\leq b\leq0$ traps the unstable branch leaving the saddle $(\eta,0)$ toward lower population. On its top edge $b'<0$. On the sloping edge, $(b+\eta a)'=\eta(c-\eta)a-a(\eta^2-a^2)/(1+a^2)>0$, so that edge is also inward. The right edge has $a'=b\leq0$. 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.
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