Boundaries of sustainability in simple and elaborate models of agricultural pest control with a pesticide and a non-toxic refuge.

In two models of pest control using a pesticidal crop along with a non-pesticidal refuge to prevent the development of resistance, we numerically compute the bifurcations that bound the region in parameter space where control is sustainable indefinitely. An exact formula for one of the bifurcation surfaces in one of the models is also found. One model is conceptual and as simple as possible.