Pest control may make the pest population explode (Q1417469)

Consider the following mathematical model for pest control \[ \dot x= x(1+x(y-1) \exp(-y))-4y,\qquad \dot y= y(x\exp (-y)-4), \] with the initial conditions \(x(0)= a\), \(y(0)= b\), where \(a,b\) are positive constants. It is shown that this model has the property that the population always converges to a unique equilibrium state, but if the death rate of the predator is increased slightly, then there are initial conditions for which the populations of both species blow up in finite time.