Additional-food predator explosion conjecture for general predator-pest models

Consider the general predator-pest model

$$\frac{dx}{dt}=F(x,y;\xi),\qquad \frac{dy}{dt}=G(x,y;\xi),$$

where $x$ is the pest population, $y$ is the predator population, $\xi$ is the quantity of additional food, and $f$ is a pest-dependent functional response. Additional-food predator explosion conjecture. If $\xi>\xi_{critical}$, then the predator population $y$ blows up in infinite time for any pest-dependent functional response $f$. The claim proposes that sufficiently large additional food can hinder biological control by causing unbounded predator growth and associated non-target effects; its status is not established by the supplied text.