Stability analysis of a tritrophic model with stage structure in the prey population

We analyze the role of the age structure of a prey in the dynamics of a tritrophic model. We study the effect of predation on a non-reproductive prey class, when the reproductive class of the prey has a defense mechanism. We consider two cases accordingly to the interaction between predator and reproductive class of the prey. In the first case, the functional response is Holling type II and it is possible to show up to two positive equilibria. When we consider a defense mechanism the functional response is Holling type IV. In both cases, we show sufficient parameter conditions to have a stable limit cycle obtained by a supercritical Hopf bifurcation. Some numerical simulations are carried out.