On the stabilizing effect of cannibalism in stage-structured population models

In this paper we give a contribution to the systematic investigation of cannibalism in predator-prey models commenced since the publication of the paper by Kohlmeier and Ebenhöh in 1995. We present a stage-structured predator-prey model and study its dynamics. We use a Hopf bifurcation analysis to prove that cycles are possible and that cannibalism suppresses these cycles; that is, when cannibalism attack rate is increased so that it passes a critical value, the coexistence steady state changes from being unstable to being stable. Numerical simulations are provided together with the mathematical analysis. Our modelling approach is based on balance arguments and a comparison with some early models which predict that a destabilizing effect of cannibalism is performed. Our results agree with the output of growth simulation for some cannibalistic copepods.