Modelling plant-pest interactions is not an obvious task since the involved processes are numerous and complex. We propose a minimal model based on trophic relations and the concept o f plant compensation capacity. We only consider three main components in our system: the plant foliar biomass, the compensation capacity, and the pest population. We prove that there exist two threshold parameters, N1 and N2, and show that the system admits different equilibria, which are locally asymptotically stable or unstable, depending on the value of the previous threshold parameters. Finally, we summarize our theoretical results in a bifurcation diagram that allows to discuss possible control strategies to lower the impacts of the pest or even to obtain a better biomass yield.