A two-dimensional stage-structured population model with nonlinear cannibalism terms is studied. We show that there is a large parameter interval where the nontrivial equilibrium of the model is the only stable attractor, but that there also exist parameter intervals where we find quasiperiodic, periodic and chaotic dynamics. Moreover, in the interplay between increasing the fecundity and increasing the cannibalism pressure, the former turns out to be a destabilizing effect while the latter tends to act in a stabilizing fashion. Finally, we have applied the model to the North Atlantic cod stock using ICES biomass estimates. Our main conclusion from this study is that the combined effect of recruitment and cannibalism may not serve as an explanation of the observed fluctuations in the cod stock.