Stabilization of an oscillating n-dimensional structured population model

We consider a model of a predator with q size-classes feeding on one resource. The resource is also modelled by a logistic function. This model may have sustained oscillations in dimension (q+1) around an unstable equilibrium. A possible control consists in harvesting every class. We show that (under good assumptions) this model can be reduced to a two-dimensional predator-prey model having sustained oscillations. We design positive controls to suppress the oscillations and to stabilize the equilibrium of the reduced and full model.