Effect of prey growth and predator cannibalism rate on the stability of a structured population model

The dynamics of a structured population model including cannibalism is analyzed. Hopf bifurcation threshold for the cannibalistic attack rate is detected. Linear and nonlinear stability analysis through the Lyapunov Direct Method is also provided. The effects of relevant parameters on the stability are discussed. In particular, cannibalism is found to have a stabilizing effect, whereas the prey growth effect is opposite. The result is emphasized by numerical simulations.